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The sides of a parallelogram are 2hati +...

The sides of a parallelogram are `2hati +4hatj -5hatk and hati + 2hatj +3hatk `. The unit vector parallel to one of the diagonals is

A

`(1)/(7)(3hati+6hatj-2hatk)`

B

`(1)/(7)(3hati-6hatj-2hatk)`

C

`(1)/(sqrt(69))(hati+2hatj+8hatk)`

D

`(1)/(sqrt(69))(-hati-2hatj+8hatk)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Let `a=2hati+4hatj-5hatk and b=hati+2hatj+3hatk`.
then, the diagonals of the parallelogram are
p=a+b
and q=b-a,
i.e., `p=3hati+6hatj-2hatk,q=-hati-2hatj+8hatk`
so, unit vectors along the diagonals are
`(1)/(7)(3hati+6hatj-2hatk) and (1)/(sqrt(69))(-1hati-2hatj+8hatk)`.
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