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

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

1.	The vector equation of the line passing through the points (1,-2,5) and (-2,1,3) isA. `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)`
Answer» Correct Answer - 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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