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

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

A

`-1`

B

`-(1)/(2)`

C

`(1)/(2)`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
B
`( 2 hat(i) + 3 hat(j) + 8 hat(k)). (-4 hat(i) + 4 hat(j) + alpha hat(k)) = 0`
` - 8 + 12 + 8 alpha = 0 rArr alpha = -(1)/(2)`
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Knowledge Check

  • 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

  • Projection of the vector 2hat(i) + 3hat(j) + 2hat(k) on the vector hat(i) - 2hat(j) + 3hat(k) is :

    A
    `(2)/(sqrt(14))`
    B
    `(1)/(sqrt(14))`
    C
    `(3)/(sqrt(17))`
    D
    `(3)/(sqrt(14))`

  • A unit vector perpendicular to each of the vectors 2hat(i) - hat(j) + hat(k ) and 3hat(i) - 4hat(i) - hat(k) is

    A
    `(1)/(sqrt3) hat(i) + (1)/(sqrt3) hat(j) - (1)/(sqrt3) hat(k)`
    B
    `(1)/(sqrt2) hat(i) + (1)/(2) hat(j) + (1)/(2) hat(k)`
    C
    `(1)/(sqrt3) hat(i) - (1)/(sqrt3) hat(j) -(1)/(sqrt3) hat(k)`
    D
    `(1)/(sqrt3) hat(i) + (1)/(3) hat(j) + (1)/(sqrt3) hat(k)`

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