Question

Find the vector that has (a) the same direction as A and twice the magnitude of A, (b) the opposite direction of a and one-third the magnitude of a, and (c) the same direction as A and magnitude 2.

(i)A=14i-15j+6k

Answer 1

(a)

$$2\vec A=28\vec i-30\vec j+12\vec k$$

(b)

$$-\dfrac{1}{3}\vec A=-\dfrac{14}{3}\vec i+5\vec j-2\vec k$$

(c)

$$|\vec A|=\sqrt{(14)^2+(-15)^2+(6)^2}=\sqrt{457}$$

$$\dfrac{2}{\sqrt{457}}\vec A=\dfrac{28}{\sqrt{457}}\vec i-\dfrac{30}{\sqrt{457}}\vec j+\dfrac{12}{\sqrt{457}}\vec k$$