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If a vector 2hat(i)+3hat(j)+8hat(k) is p...

If a vector `2hat(i)+3hat(j)+8hat(k)` is perpendicular to the vector `4hat(j)-4hat(i)+alpha hat(k)`. 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
We are given
`vec(a)= 2hat(i)+3hat(j)+8hat(k), vec(b)= 4hat(j)-4hat(i)+alpha hat(k)`
According to the above hypothesis,
If `vec(a)_|_ vec(b)`, then dot product of Vector should be zero
`vec(a).vec(b)=0`
`implies (2hat(i)+3hat(j)+8hat(k))(-4hat(i)+4hat(j)+alpha hat(k))=0`
`implies -8+12+8 alpha=0implies 8 alpha = -4`
`:. alpha= -4/8= -1/2`
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