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The two adjacent sides of a parallelogra...

The two adjacent sides of a parallelogram are `2hati+4hatj-5hatk and hati+2hatj+3hatk`. Find the unit vectors along the diagonals of the parallelogram.

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `AB+BD=AD`
`BD=AD-AB`
`implies =(hati+2hatj+3hatk)-(2hati+4hatj-5hatk)`
`=-hati-2hatj+8hatk`
Hence, unit vector in the direction of BD is
`(-hati-2hatj+8hatk)/(|-hati-2hatj+8hatk|)=(-hati-2hatj+8hatk)/(sqrt(69))`.
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
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  9. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

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  13. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

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  17. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

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  18. If the resultant of two forces is equal in magnitude to one of the ...

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  19. If vec b is a vector whose initial point divides the join of 5 hat ...

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