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The vector equation of the line (x+2)/(3...

The vector equation of the line `(x+2)/(3)=(1-y)/(-2)=(z-5)/(7) ` is

A

`r=(3hati-2hatj+7hatk)+lambda(-2hati+hatj+5hatk)`

B

`r=(-2hati+hatj+5hatk)+lambda(3hati-2hatj+7hatk)`

C

`r=(3hati-2hatj+7hatk)+lambda(2hati+hatj-5hatk)`

D

`r=(2hati+hatj+5hatk)+lambda(3hati+2hatj+7hatk)`

Text Solution

Verified by Experts

The correct Answer is:
B
The direction ratios of the given line are (3,-2,7). `therefore` The given line is parallel to `3hati-2hatj+7hatk`
From the cartesian equation of the given line, it is clear that is passes through the points (-2,1,5).
`therefore` The vector equation of line is
`r=(-2hati+hatj+5hatk)+lambda(3hati-2hatj+7hatk)`
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