Question

Find the vector equation of a line passing through the points A(3, 4, –7) and B(6, –1, 1).

Answer 1

The vector equation of a line passing through the points having position vectors `bara` and `barb` is given 

by `barr=bara+lambda(barb-bara)`

`Here, bara=3hati+4hatj-7hatk and barb=6hati-hatj+hatk` 

the vector equation of the line passing through A (3, 4, -7) and B (6,-1, 1) is

`barr=(3hati+4hatj-7hatk)+lambda[(6hati-hatj+hatk)-(3hati+4hatj-7hatk)]`

`barr=(3hati+4hatj-7hatk)+lambda(3hati-5hatj+8hatk)`