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If ABCD is a parallelogram and the posit...

If ABCD is a parallelogram and the position vectors of A,B and C are `hati+3hatj+5hatk, hati+hatj+hatk and 7 hati+7hatj+7hatk`, then the position vector of D will be

A

`7hati+5hatj+3hatk`

B

`7hati+9hatj+11hatk`

C

`9hati+11hatj+13hatk`

D

`8hati+8hatj+8hatk`

Text Solution

Verified by Experts

The correct Answer is:
B
Let position vector of D is `xhati+yhatj+zhatk`, then AB=DC.
`-2hatj-4hatk=(7-x)hati+(7-y)hatj+(7-z)hatk`
`impliesx=7,y=9 and z=11`
Hence, position vector of D will be `7hati+9hatj+11hatk`.
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