Maths-
General
Easy

Question

If r. i equals r. j equals r. k and vertical line r vertical line equals 3 comma then r equals

  1. plus-or-minus 3 left parenthesis i plus j plus k right parenthesis    
  2. plus-or-minus fraction numerator 1 over denominator 3 end fraction left parenthesis i plus j plus k right parenthesis    
  3. plus-or-minus fraction numerator 1 over denominator square root of 3 end fraction left parenthesis i plus j plus k right parenthesis    
  4. plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis    

The correct answer is: plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis


    Let r equals x i plus y j plus z k. Since r. i equals r. j equals r. k
    rightwards double arrow x equals y equals z .....(i)
    Also vertical line r vertical line equals square root of x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent end root equals 3 rightwards double arrow x equals plus-or-minus square root of 3, {By (i)}
    Hence the required vector r equals plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis.
    Trick : As the vector plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis satisfies both the conditions.

    Related Questions to study

    General
    Maths-

    If three points A, B and C have position vectors left parenthesis 1 comma x comma 3 right parenthesis comma left parenthesis 3 , 4 comma 7 right parenthesis and a p plus b q plus c r equals 1 respectively and if they are collinear, then left parenthesis x comma y right parenthesis equals

    If three points A, B and C have position vectors left parenthesis 1 comma x comma 3 right parenthesis comma left parenthesis 3 , 4 comma 7 right parenthesis and a p plus b q plus c r equals 1 respectively and if they are collinear, then left parenthesis x comma y right parenthesis equals

    Maths-General
    General
    Maths-

    The points with position vectors 60 i plus 3 j, 40 i minus 8 j comma , a i minus 52 j are collinear, if a equals

    The points with position vectors 60 i plus 3 j, 40 i minus 8 j comma , a i minus 52 j are collinear, if a equals

    Maths-General
    General
    Maths-

    If O is origin and C is the mid point of A left parenthesis 2 comma negative 1 right parenthesis and B left parenthesis negative 4 , 3 right parenthesis. Then value of Error converting from MathML to accessible text. is

    If O is origin and C is the mid point of A left parenthesis 2 comma negative 1 right parenthesis and B left parenthesis negative 4 , 3 right parenthesis. Then value of Error converting from MathML to accessible text. is

    Maths-General
    parallel
    General
    Maths-

    If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is

    If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is

    Maths-General
    General
    Maths-

    Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that 2 A C equals C O comma C D is parallel to OB and Error converting from MathML to accessible text. then Error converting from MathML to accessible text. is equal to

    Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that 2 A C equals C O comma C D is parallel to OB and Error converting from MathML to accessible text. then Error converting from MathML to accessible text. is equal to

    Maths-General
    General
    Maths-

    Solution of the inequation log subscript 0.1 end subscript invisible function application open parentheses log subscript 2 end subscript invisible function application fraction numerator x to the power of 2 end exponent plus 1 over denominator vertical line x minus 1 vertical line end fraction close parentheses < 0 contains the interval

    Solution of the inequation log subscript 0.1 end subscript invisible function application open parentheses log subscript 2 end subscript invisible function application fraction numerator x to the power of 2 end exponent plus 1 over denominator vertical line x minus 1 vertical line end fraction close parentheses < 0 contains the interval

    Maths-General
    parallel
    General
    Maths-

    If the position vector of one end of the line segment AB be 2 i plus 3 j minus k and the position vector of its middle point be 3 left parenthesis i plus j plus k right parenthesis comma then the position vector of the other end is

    If the position vector of one end of the line segment AB be 2 i plus 3 j minus k and the position vector of its middle point be 3 left parenthesis i plus j plus k right parenthesis comma then the position vector of the other end is

    Maths-General
    General
    Maths-

    If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that Error converting from MathML to accessible text. is

    If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that Error converting from MathML to accessible text. is

    Maths-General
    General
    Maths-

    What should be added in vector a equals 3 i plus 4 j minus 2 k to get its resultant a unit vector i

    What should be added in vector a equals 3 i plus 4 j minus 2 k to get its resultant a unit vector i

    Maths-General
    parallel
    General
    Maths-

    In the figure, a vector x satisfies the equation x minus w equals v. Then x =

    In the figure, a vector x satisfies the equation x minus w equals v. Then x =

    Maths-General
    General
    Maths-

    If the position vectors of the vertices A, B, C of a triangle ABC are 7 j plus 10 k comma negative i plus 6 j plus 6 k and negative 4 i plus 9 j plus 6 k respectively, the triangle is

    If the position vectors of the vertices A, B, C of a triangle ABC are 7 j plus 10 k comma negative i plus 6 j plus 6 k and negative 4 i plus 9 j plus 6 k respectively, the triangle is

    Maths-General
    General
    Maths-

    If p equals 7 i minus 2 j plus 3 k and q equals 3 i plus j plus 5 k comma then the magnitude of p minus 2 q is

    If p equals 7 i minus 2 j plus 3 k and q equals 3 i plus j plus 5 k comma then the magnitude of p minus 2 q is

    Maths-General
    parallel
    General
    Maths-

    If the points left parenthesis a u to the power of 2 end exponent comma   2 a u right parenthesis and left parenthesis a v to the power of 2 end exponent comma   2 a v right parenthesis are the extremities of a focal chord of the parabola y to the power of 2 end exponent equals 4 a x, then

    If the points left parenthesis a u to the power of 2 end exponent comma   2 a u right parenthesis and left parenthesis a v to the power of 2 end exponent comma   2 a v right parenthesis are the extremities of a focal chord of the parabola y to the power of 2 end exponent equals 4 a x, then

    Maths-General
    General
    Maths-

    The locus of the middle point of the intercept of the tangents drawn from an external point to the ellipse x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 2 between the co-ordinates axes, is

    The locus of the middle point of the intercept of the tangents drawn from an external point to the ellipse x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 2 between the co-ordinates axes, is

    Maths-General
    General
    Physics-

    An isolated north pole of mass 2gm and pole strength 10 A-m is kept in a uniform magnetic field of induction 4 cross times 10 to the power of negative 3 end exponent text end text T. The force experienced by the pole is

    An isolated north pole of mass 2gm and pole strength 10 A-m is kept in a uniform magnetic field of induction 4 cross times 10 to the power of negative 3 end exponent text end text T. The force experienced by the pole is

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.