Home
Class 12
MATHS
If a=3hati-hatj+5hatk and b=hati+2hatj-3...

If `a=3hati-hatj+5hatk and b=hati+2hatj-3hatk` are given vector, A vector c which is perpenduclar to Z-axis satisfying `c*a=9 and c*b=-4`. If inclination of c with X-axis and Y-axis is `alpha and beta` respectively, then which of the following is not true?

A

`alpha gt pi/4`

B

`beta gt pi/2`

C

`alpha gt pi/2`

D

`beta lt pi/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`vecc` lies in xy-plane
`therefore vecc=xhati+yhatj`
From the given conditions `3x-y=9` and `x+2y=-4`
Solving we get `vecc=2hati-3hatj`
`therefore alpha=cos^(-1)(2/sqrt(13)),beta=cos^(-1)(-3/sqrt(13))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

  • ELLIPSE

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|49 Videos

Similar Questions

Explore conceptually related problems

If veca=3hati-hatj+5hatk and vecb=hati+2hatj-3hatk are given vectors. A vector vecc which is perpendicular to z-axis satisfying vecc.veca=9 and vecc.vecb=-4 . If inclination of vecc with x-axis and y-axis and y-axis is alpha and beta respectively, then which of the following is not true?

Let a=2hati+hatj+hatk,b=hati+2hatj-hatk and c is a unit vector coplanar to them. If c is perpendicular to a, then c is equal to

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If a=hati+2hatj+3hatk,b=-hati+2hatj+hatk and c=3hati+hatj , then the unit vector along its resultant is

Let vec a=4hati+5hatj-hatk, vecb = hati -4hatj+5hatk and vec c=3hati+hatj-hatk . Find a vector vec d which is perpendicular to both vec c and vec b and vec d.vec a=21

If a=hati+2hatj+3hatk,b=-hati+2hatj+hatk and c=3hati+hatj . If (a+tb) bot c , then t is equal to

If hati,hatj and hatk are unit vectors along X,Y & Z axis respectively, then tick the wrong statement:

If the vectors a hati + 3 hatj - 2 hatk and 3 hati - 4 hatj + b hatk are collinear, then (a,b) =

if A = 2hati - 3hatj+7hatk, B = hati + 2hatj and C=hatj - hatk . Find A(BxxC)

if A = 2hati - 3hatj+7hatk, B = hati + 2hatj and C=hatj - hatk . Find A(BxxC)