Question

A= 2i + 3j - k, B= 4i + 2j - 2k, Find a vector x parallel to A but has the magnitude of B ?

Answer 1

$$A=\sqrt{2^2+3^2+1^2}=\sqrt{14}\\ B=\sqrt{4^2+2^2+2^2}=2\sqrt{6}$$

Thus,

$$\vec{C}=\frac{2\sqrt{6}}{\sqrt{14}}(2\vec{i}+3\vec{j}-\vec{k})\\ \vec{C}=2\sqrt{\frac{3}{7}}(2\vec{i}+3\vec{j}-\vec{k})$$