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If veca=3hati-hatj+5hatk and vecb=hati+2...

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?

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))`
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