Question

Find the vector of magnitude 11 units in the direction opposite to pqwhere p(1 3 2) and q(-1 0 8)

Answer 1

The vector with initial point P(1,3,2) And terminal point Q(-1,0,8) is given by

PQ = (-1-1)i + (0-3)j + (8-2)k

PQ = - 2i - 3j + 6k

QP = -PQ = - 1(- 2i - 3j + 6k)

QP vector = 2i +3j - 6k

IQPI = $\sqrt{(2^2) + (3^2) + (-6^2)}$

IQPI = $\sqrt{49}$ = 7

Therefore unit vector in direction of QP vector is given by

QP unit vector = QP vector/IQPI

QP unit vector = (2i +3j - 6k)/7

QP unit vector = (2/7) i + (3/7) j - (6/7) k

Hope my answer and picture attached will satisfy you.