Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Let u = i + j, v = i – j and w = i + 2j + 3k. If n is a unit vector such that u.n = 0 and v.n = 0 then $vertical line w. n vertical line$ is equal to

0
1
2
3

The correct answer is: 3

$because n$ is perpendicular to u and v
$n equals u cross times v$
$n equals fraction numerator open vertical bar table row i j k row 1 1 0 row 1 cell negative 1 end cell 0 end table close vertical bar over denominator square root of 2 cross times square root of 2 end fraction equals fraction numerator negative 2 k over denominator 2 end fraction equals negative k$
$vertical line w. n vertical line equals vertical line left parenthesis i plus 2 j plus 3 k right parenthesis. left parenthesis negative k right parenthesis vertical line equals vertical line minus 3 vertical line equals 3$ .

Related Questions to study

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

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

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

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

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

parallel

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

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

parallel

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

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

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

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

parallel

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

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:

parallel

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

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

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.