Question

i have 3 vectors PQ[-2,-4,-1] QR[2,-2,2-t] and [-10, -2,-8-3t], but now i need to find t so that the angle PQR equals 90 degrees, how to start?

Answer 1

what is [-10, -2,-8-3t] then?

Answer 2

angle PQR is formed by PQ and QR, the third vector is irrelevant.

given two vectors a,b, then a and b are perpendicular if
a dot b = 0

PQ dot QR = 0, solve for t

Answer 3

what do you mean what is [-10,-2,-8-3t]?=S

Answer 4

He's asking why they gave the the last vector, we do not need it to solve this.

Take your two vectors \(PQ[-2,-4,-1]\) and \(QR[2,-2,2-t]\), then the angle between them will be 90 degrees if the dot product of them is zero, So we need,
\(-2*2+-4*-2+-1*(2-t)=0\)
solve for \(t\)