The position vectors of `P and Q` are `5hati+4hatj+ahatk and -hati+2hatj-2hatk`, respectively. If the distance between them is 7, then find the value of `a`.

Explanation

Given points are `P(5hati+4hatj+ahatk) and Q(-hati+2hatj-2hatk)`
Now `" "vec(PQ)= (-hati+2hatj-2hatk)-(5hati+4hatj+ahatk)`
`" "=(-6hati-2hatj-(2+a)hatk)`
Given `|vec(PQ)|=7`
`therefore" "sqrt(36+4+(a+2)^(2))=7`
or `" "(a+2)^(2)=9 `
or `" "a+2=pm3`
or `" "a=-5, 1`.