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The vector equation of the line passing ...

The vector equation of the line passing through the points (1,-2,5) and (-2,1,3) is

A

`r=-2hati +hatj + 3hatk + lambda (3hati-3hatj+2hatk)`

B

`r=-2hati -hatj + 3hatk + lambda (hati+3hatj-5hatk)`

C

`r=-hati -2hatj + 5hatk + lambda (-2hati-hatj+3hatk)`

D

`r=-2hati +hatj + 3hatk + lambda (hati-2hatj+5hatk)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `A-=(-2,1,3) and B-=(1,-2,5)`
Then `a=-2hati+hatj+3hatk and b=hati-2hatj+5hatk`
`therefore b-a=3hati-3hatj+2hatk`
Let r be the position vector of any point on the line. Then, the vector equation of the line is
`r=-2hati+hatj+3hatk+lambda(3hati-3hatj+2hatk)`
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