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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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Let `R_(1)=2hati+4hatj-5hatk`
and `R_(2)=hati+2hatj+3hatk`

`:.R("along"AC)`
`=R_(1)+R_(2)`
`=3hati+6hatj-2hatk`
`:.a("unit vector along"AC)`
`=R/(|R|)=(3hati+6hatj-2hatk)/(sqrt(9+36+4))`
`=1/7(3hati+6hatj-2hatk)`
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