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If a vector 2hati +3hatj +8hatk is perpe...

If a vector `2hati +3hatj +8hatk` is perpendicular to the vector `4hati -4hatj + alphahatk,` then the value of `alpha` is

A

`-1`

B

`(1)/(2)`

C

`-(1)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Given vectors can be reqritten as `vecA=2hati+3hatj+8hatk` and `vecB=-4hati+4hatj+alphahatk`
Dot product of these vectors should be equal to zero because
they are perpendicular.
`vecA.vecB=-8+12+8alpha=0implies8alpha-4impliesalpha=(-1)/(2)`
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