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Maths-

General

Easy

Question

Angle between the line $r equals left parenthesis i plus 2 j minus k right parenthesis plus lambda rightwards arrow over short leftwards arrow left parenthesis i minus j plus k right parenthesis$ and the normal to the plane $r. left parenthesis 2 i minus j plus k right parenthesis equals 4$ is

${s i n}^{- 1} (\frac{2 \sqrt{2}}{3})$
${c o s}^{- 1} (\frac{2 \sqrt{2}}{3})$
${t a n}^{- 1} (\frac{2 \sqrt{2}}{3})$
${c o t}^{- 1} (\frac{2 \sqrt{2}}{3})$

The correct answer is: $s i n to the power of negative 1 end exponent open parentheses fraction numerator 2 square root of 2 over denominator 3 end fraction close parentheses$

The plane is $2 x minus y plus z equals 4$ and the line is $fraction numerator x minus 1 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator negative 1 end fraction equals fraction numerator z plus 1 over denominator 1 end fraction$
$therefore sin invisible function application theta equals fraction numerator 2 plus 1 plus 1 over denominator square root of 6 square root of 3 end fraction equals fraction numerator 4 over denominator square root of 18 end fraction equals fraction numerator 2 square root of 2 over denominator 3 end fraction rightwards double arrow theta equals sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 2 square root of 2 over denominator 3 end fraction close parentheses$ .

Related Questions to study

$left square bracket left parenthesis a cross times b right parenthesis cross times left parenthesis b cross times c right parenthesis left parenthesis b cross times c right parenthesis cross times left parenthesis c cross times a right parenthesis left parenthesis c cross times a right parenthesis cross times left parenthesis a cross times b right parenthesis right square bracket equals$

$left square bracket left parenthesis a cross times b right parenthesis cross times left parenthesis b cross times c right parenthesis left parenthesis b cross times c right parenthesis cross times left parenthesis c cross times a right parenthesis left parenthesis c cross times a right parenthesis cross times left parenthesis a cross times b right parenthesis right square bracket equals$

If $u equals 2 i plus 2 j minus k$ and $v equals 6 i minus 3 j plus 2 k comma$ then a unit vector perpendicular to both u and v is

If $u equals 2 i plus 2 j minus k$ and $v equals 6 i minus 3 j plus 2 k comma$ then a unit vector perpendicular to both u and v is

The equation of plane passing through a point $A left parenthesis 2 comma negative 1 , 3 right parenthesis$ and parallel to the vectors $a equals left parenthesis 3 , 0 comma negative 1 right parenthesis$ and $b equals left parenthesis negative 3 , 2 comma 2 right parenthesis$ is

The equation of plane passing through a point $A left parenthesis 2 comma negative 1 , 3 right parenthesis$ and parallel to the vectors $a equals left parenthesis 3 , 0 comma negative 1 right parenthesis$ and $b equals left parenthesis negative 3 , 2 comma 2 right parenthesis$ is

parallel

The equation of the plane passing through the points $left parenthesis negative 1 comma negative 2 , 0 right parenthesis comma left parenthesis 2 , 3 comma 5 right parenthesis$ and parallel to the line
$r equals negative 3 j plus k plus lambda left parenthesis 2 i plus 5 j minus k right parenthesis$ is

The equation of the plane passing through the points $left parenthesis negative 1 comma negative 2 , 0 right parenthesis comma left parenthesis 2 , 3 comma 5 right parenthesis$ and parallel to the line
$r equals negative 3 j plus k plus lambda left parenthesis 2 i plus 5 j minus k right parenthesis$ is

The distance from the point $negative i plus 2 j plus 6 k$ to the straight line through the point (2, 3, –4) and parallel to the vector $6 i plus 3 j minus 4 k$ is

The distance from the point $negative i plus 2 j plus 6 k$ to the straight line through the point (2, 3, –4) and parallel to the vector $6 i plus 3 j minus 4 k$ is

The length of the perpendicular from the origin to the plane passing through three non-collinear points $a comma b comma c$ is

The length of the perpendicular from the origin to the plane passing through three non-collinear points $a comma b comma c$ is

parallel

A vector $n$ of magnitude 8 units is inclined to x-axis at $4 5 to the power of o end exponent$ , y-axis at $6 0 to the power of o end exponent$ and an acute angle with z-axis. If a plane passes through a point $left parenthesis square root of 2 comma negative 1 , 1 right parenthesis$ and is normal to $n$ , then its equation in vector form is

A vector $n$ of magnitude 8 units is inclined to x-axis at $4 5 to the power of o end exponent$ , y-axis at $6 0 to the power of o end exponent$ and an acute angle with z-axis. If a plane passes through a point $left parenthesis square root of 2 comma negative 1 , 1 right parenthesis$ and is normal to $n$ , then its equation in vector form is

$fraction numerator text d end text over denominator text dx end text end fraction open square brackets s i n open parentheses l o g open parentheses s i n e to the power of x to the power of 2 end exponent end exponent close parentheses close parentheses close square brackets$ =

$fraction numerator text d end text over denominator text dx end text end fraction open square brackets s i n open parentheses l o g open parentheses s i n e to the power of x to the power of 2 end exponent end exponent close parentheses close parentheses close square brackets$ =

If $square root of T a n y end root$ = $e to the power of c o s 2 x end exponent. s i n x comma blank t h e n blank fraction numerator text dy end text over denominator text dx end text end fraction$ =

If $square root of T a n y end root$ = $e to the power of c o s 2 x end exponent. s i n x comma blank t h e n blank fraction numerator text dy end text over denominator text dx end text end fraction$ =

parallel

The line $chi plus gamma equals 2$ is tangent to tthe curve $chi to the power of 2 end exponent equals 3 minus 2 gamma$ at its point

The line $chi plus gamma equals 2$ is tangent to tthe curve $chi to the power of 2 end exponent equals 3 minus 2 gamma$ at its point

In general calcium carbonate is not soluble in water but by the addition of carbon dioxide to it, it becomes soluble. This is because:

In general calcium carbonate is not soluble in water but by the addition of carbon dioxide to it, it becomes soluble. This is because:

The correct stability order for the following species is:
I)
II)
III)
IV)

The correct stability order for the following species is:
I)
II)
III)
IV)

Chemistry-General

parallel

The point (4,3) is translated to the point (3,1) and then axes rotated through 30º about the origin then the new position of point is

The point (4,3) is translated to the point (3,1) and then axes rotated through 30º about the origin then the new position of point is

The arrangement of the following in ascending order of angle of rotation to eliminate xy term in the following equations.
i) 2 $text x end text to the power of 2 end exponent$ +5xy+2 $text y end text to the power of 2 end exponent$ +5x+7y+1=0
ii) 2 $text x end text to the power of 2 end exponent$ + $square root of text 3 end text end root$ xy+3 $text y end text to the power of 2 end exponent$ = 9
iii) 9 $x to the power of 2 end exponent$ +2 $square root of text 3 end text end root$ xy+7 $text y end text to the power of 2 end exponent$ = 10

The arrangement of the following in ascending order of angle of rotation to eliminate xy term in the following equations.
i) 2 $text x end text to the power of 2 end exponent$ +5xy+2 $text y end text to the power of 2 end exponent$ +5x+7y+1=0
ii) 2 $text x end text to the power of 2 end exponent$ + $square root of text 3 end text end root$ xy+3 $text y end text to the power of 2 end exponent$ = 9
iii) 9 $x to the power of 2 end exponent$ +2 $square root of text 3 end text end root$ xy+7 $text y end text to the power of 2 end exponent$ = 10

If the distance between the two given points is 2 units and the points are transferred by shifting the origin to (2,2) then the distance between the points in their new position is

If the distance between the two given points is 2 units and the points are transferred by shifting the origin to (2,2) then the distance between the points in their new position is

parallel

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