Question

It is a vector question?

Answer 1

`p= 6.5 \ \`, and `q= -1.5`,

Explanation:

We have:

`bbvec(OA) = ((0),(2),(-3)) \ \`, `bbvec(OB) = ((2),(5),(-2)) \ \` and `bbvec(OC) = ((3),(p),(q))`

And so we can compute the vector `bbvec(AB)`,

`bbvec(AB) = bbvec(OB) - bbvec(OA) = ((2),(5),(-2)) - ((0),(2),(-3)) = ((2),(3),(1))`

Similarly, we can compute the vector `bbvec(BC)`,

`bbvec(BC) = bbvec(OC) - bbvec(OB) = ((3),(p),(q)) - ((2),(5),(-2)) = ((1),(p-5),(q+2))`

As ABC is a straight line then, for some constant `lamda`,

`bbvec(AB) = lamda bbvec(BC)`

Hence we have:

`((2),(3),(1)) = lamda ((1),(p-5),(q+2))`

Equating components:

`R1: 2 = lamda`,
`R2: 3=lamda(p-5) => p-5=3/2 => p= 6.5`,
`R3: 1=lamda(q+2) => q+2=1/2 => q= -1.5`,