Maths-
General
Easy

Question

If the sides be a, b, c then (r + r1) tanfraction numerator B minus C over denominator 2 end fraction+ (r + r2) tanfraction numerator C minus A over denominator 2 end fraction+ (r + r3) tanfraction numerator A minus B over denominator 2 end fraction =

  1. 1    
  2. 0    
  3. 2    
  4. 4    

The correct answer is: 0

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If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

Therefore, the radius of the circle DEF is R/2.

If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

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Therefore, the radius of the circle DEF is R/2.

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In an equilateral triangle of side 2 square root of 3 cms, the circum radius is -

The circumradius is 2cm.

In an equilateral triangle of side 2 square root of 3 cms, the circum radius is -

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The circumradius is 2cm.

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If the lines text end text fraction numerator x over denominator 1 end fraction equals fraction numerator y over denominator 2 end fraction equals fraction numerator z over denominator 3 end fraction comma fraction numerator x minus 1 over denominator 3 end fraction equals fraction numerator y minus 2 over denominator negative 1 end fraction equals fraction numerator z minus 3 over denominator 4 end fraction text end textand text end text fraction numerator x plus k over denominator 3 end fraction equals fraction numerator y minus 1 over denominator 2 end fraction equals fraction numerator z minus 2 over denominator h end fraction text end textare concurrent then

If the lines text end text fraction numerator x over denominator 1 end fraction equals fraction numerator y over denominator 2 end fraction equals fraction numerator z over denominator 3 end fraction comma fraction numerator x minus 1 over denominator 3 end fraction equals fraction numerator y minus 2 over denominator negative 1 end fraction equals fraction numerator z minus 3 over denominator 4 end fraction text end textand text end text fraction numerator x plus k over denominator 3 end fraction equals fraction numerator y minus 1 over denominator 2 end fraction equals fraction numerator z minus 2 over denominator h end fraction text end textare concurrent then

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text If  end text stack a with rightwards arrow on top equals i plus j minus k comma stack b with rightwards arrow on top equals i minus j plus k comma stack c with rightwards arrow on top is a unit vector such that stack c with rightwards arrow on top times stack a with rightwards arrow on top equals 0 comma left square bracket stack c with rightwards arrow on top stack a with rightwards arrow on top stack b with rightwards arrow on top right square bracket equals0 then a unit vector text end text stack d with rightwards arrow on top perpendicular to text  both  end text stack a with rightwards arrow on top text  and  end text stack c with rightwards arrow on top text end text text is end text

text If  end text stack a with rightwards arrow on top equals i plus j minus k comma stack b with rightwards arrow on top equals i minus j plus k comma stack c with rightwards arrow on top is a unit vector such that stack c with rightwards arrow on top times stack a with rightwards arrow on top equals 0 comma left square bracket stack c with rightwards arrow on top stack a with rightwards arrow on top stack b with rightwards arrow on top right square bracket equals0 then a unit vector text end text stack d with rightwards arrow on top perpendicular to text  both  end text stack a with rightwards arrow on top text  and  end text stack c with rightwards arrow on top text end text text is end text

maths-General
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The reflection of the point (2, –1, 3) in the plane 3x – 2y – z = 9 is :

The reflection of the point (2, –1, 3) in the plane 3x – 2y – z = 9 is :

maths-General
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A, B, C & D are four points in a plane with position vectors stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top & stack d with rightwards arrow on top respectively such that left parenthesis stack a with rightwards arrow on top minus stack d with rightwards arrow on top right parenthesis times left parenthesis stack b with rightwards arrow on top minus stack c with rightwards arrow on top right parenthesis equals left parenthesis stack b with rightwards arrow on top minus stack d with rightwards arrow on top right parenthesis times left parenthesis stack c with rightwards arrow on top minus stack a with rightwards arrow on top right parenthesis equals 0 Then for the triangle ABC, D is its:

A, B, C & D are four points in a plane with position vectors stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top & stack d with rightwards arrow on top respectively such that left parenthesis stack a with rightwards arrow on top minus stack d with rightwards arrow on top right parenthesis times left parenthesis stack b with rightwards arrow on top minus stack c with rightwards arrow on top right parenthesis equals left parenthesis stack b with rightwards arrow on top minus stack d with rightwards arrow on top right parenthesis times left parenthesis stack c with rightwards arrow on top minus stack a with rightwards arrow on top right parenthesis equals 0 Then for the triangle ABC, D is its:

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Equation of the angle bisector of the angle between the lines fraction numerator x minus 1 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus 3 over denominator 1 end fraction fraction numerator x minus 1 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus 3 over denominator negative 1 end fraction text  is : end text

Equation of the angle bisector of the angle between the lines fraction numerator x minus 1 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus 3 over denominator 1 end fraction fraction numerator x minus 1 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z minus 3 over denominator negative 1 end fraction text  is : end text

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The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where A º (3, –2, 1) ; B º (3, 1, 5); C º (4, 0, 3) and D º (1, 0, 0) is -

The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where A º (3, –2, 1) ; B º (3, 1, 5); C º (4, 0, 3) and D º (1, 0, 0) is -

maths-General
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Four coplanar forces are applied at a point O. Each of them is equal to k and the angle between two consecutive forces equals 45º as shown in the figure. Then the resultant has the magnitude equal to :

Four coplanar forces are applied at a point O. Each of them is equal to k and the angle between two consecutive forces equals 45º as shown in the figure. Then the resultant has the magnitude equal to :

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text Let  end text stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top text end textbe vectors of length 3,4,5 respectively. text Let  end text stack a with rightwards arrow on top text end textbe perpendicular to text end text stack b with rightwards arrow on top plus stack c with rightwards arrow on top comma stack b with rightwards arrow on top text  to  end text stack c with rightwards arrow on top plus stack a with rightwards arrow on top text end textand text c to  end text stack a with rightwards arrow on top plus stack b with rightwards arrow on top text  . Then  end text vertical line stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack c with rightwards arrow on top vertical line is equal to :

text Let  end text stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top text end textbe vectors of length 3,4,5 respectively. text Let  end text stack a with rightwards arrow on top text end textbe perpendicular to text end text stack b with rightwards arrow on top plus stack c with rightwards arrow on top comma stack b with rightwards arrow on top text  to  end text stack c with rightwards arrow on top plus stack a with rightwards arrow on top text end textand text c to  end text stack a with rightwards arrow on top plus stack b with rightwards arrow on top text  . Then  end text vertical line stack a with rightwards arrow on top plus stack b with rightwards arrow on top plus stack c with rightwards arrow on top vertical line is equal to :

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text If  end text vertical line stack a with rightwards arrow on top vertical line equals 5 comma vertical line stack a with rightwards arrow on top minus stack b with rightwards arrow on top vertical line equals 8 text end textand vertical line stack a with rightwards arrow on top plus stack b with rightwards arrow on top vertical line equals 10 text  , then  end text vertical line stack b with rightwards arrow on top vertical line is equal to :

text If  end text vertical line stack a with rightwards arrow on top vertical line equals 5 comma vertical line stack a with rightwards arrow on top minus stack b with rightwards arrow on top vertical line equals 8 text end textand vertical line stack a with rightwards arrow on top plus stack b with rightwards arrow on top vertical line equals 10 text  , then  end text vertical line stack b with rightwards arrow on top vertical line is equal to :

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If ABCDEF is a regular hexagon and if stack A B with bar on top plus stack A C with rightwards arrow on top plus stack A D with rightwards arrow on top plus stack A E with rightwards arrow on top plus stack A F with rightwards arrow on top equals lambda stack A D with bar on top comma text end textthen text end text lambda text  is - end text

If ABCDEF is a regular hexagon and if stack A B with bar on top plus stack A C with rightwards arrow on top plus stack A D with rightwards arrow on top plus stack A E with rightwards arrow on top plus stack A F with rightwards arrow on top equals lambda stack A D with bar on top comma text end textthen text end text lambda text  is - end text

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