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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
Given Vectors can be rewritten as `vec(A)= 2hat(i)+3hat(j)+8hat(k)` and `vec(B)= -4hat(i)+4hat(j)+alpha hat(k)`
Dot product of these Vectors should be equal to Zero because they are perpendicular
`:. vec(A).vec(B)= -8+12+8alpha= 0implies 8 alpha= -4implies alpha= -1//2`
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Knowledge Check

  • If a vector 2 hat (i) + 3 hat(j) + 8 hat(k) is perpendicular to the vector - 4 hat(i) + 4 hat(j) + alpha(k) . Then the value of alpha is

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    `-1`
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    `(1)/(2)`
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    C
    1
    D
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  • Projection of the vector 2hat(i) + 3hat(j) + 2hat(k) on the vector hat(i) - 2hat(j) + 3hat(k) is :

    A
    `(2)/(sqrt(14))`
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