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The vector equationm of the line (x-5)/(...

The vector equationm of the line `(x-5)/(3)=(y+4)/(7)=(z-6)/(2)` is

A

`r=3hati -7hatj -2hatk+lambda(5hati -4hatj +6hatk)`

B

`r=5hati +4hatj +6hatk+lambda(3hati -7hatj +2hatk)`

C

`r=3hati +7hatj +2hatk+lambda(5hati -4hatj +6hatk)`

D

`r=5hati -4hatj +6hatk+lambda(3hati +7hatj +2hatk)`

Text Solution

Verified by Experts

The correct Answer is:
D
The direction ratios of the given line are (3,7,2). `therefore` The given line is parallel to `3hati+7hatj+2hatk`
From the cartesian equation of the given line, it is clear that is passes through the points (5,-4,6).
The vector equation of the line is `r=5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk)`
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