Find a unit vector with positive first coordinate that is or

Solution

First find two directional vectors for the plane from the three given points P = (-4, 5, 4), Q = (-1, 8, 7), and R = (-1, 8, 8). PQ = = <-1+4, 8-5, 7-4> = <3, 3, 3> PR = = <-1+4, 8-5, 8-4> = <3, 3, 4> To find a vector n, orthogonal to both of them take the cross product. n = PQ X PR = <3, 3, 3> X <3, 3, 4> = <3, -3, 0> To find a unit vector, divide by the n by its magnitude. || n || = v[3² + (-3)² + 0²] = v(9 + 9 + 0) = v18 = 3v2 desire unit vector is n / || n || = <3, -3, 0> / (3v2) = <1/v2, -1/v2, 0> u can take help from this