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What is the value of a, if two vectors v...

What is the value of a, if two vectors `vec P =hati+12 hatj+hatk and vec Q =2hati-ahatj+4hatk` are perpendicular to each other ?

A

1

B

`(1)/(2)`

C

`-(1)/(2)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
If `vec P bot vec Q," then "vec P cdot vec Q=0`
`therefore 0 =(hati +12hatj+hatk) cdot (2hati - a hatj+4hatk)`
`=(1xx2) +12 xx (-a) +1xx4`
`0=6-12 a" "therefore 12 a =6" or "a=(1)/(2)`
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