The vectors ${\mathbf{a}}$, ${\mathbf{b}}$ and ${\mathbf{c}}$ are given by $\mathbf{a}=3\mathbf{i}+4

Question

The vectors ${\mathbf{a}}$, ${\mathbf{b}}$ and ${\mathbf{c}}$ are given by $\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}$, $\mathbf{b}=-\mathbf{i}+\mathbf{j}-\mathbf{k}$, $\mathbf{c}=2\mathbf{i}-\mathbf{j}+2\mathbf{k}$ respectively. Find the unit vector in the direction of ${\mathbf{a}}$. [1] Find the unit vectors parallel to ${\mathbf{b}}$. [2] Find the angle between the vectors ${\mathbf{b}}$ and ${\mathbf{c}}$, giving your answer to the nearest $0.1{}^\circ $. [2] Find the vector of magnitude $5$ in the direction of ${\mathbf{c}}$. [2]

Accepted Answer

(a) (1/5√2)(3,4,5); (b) ±(1/√3)(-1,1,-1); (c) 164.2°; (d) (5/3)(2,-1,2)

JPJC Vectors Tutorial 1(a) Q1

JPJC Vectors Tutorial 1(a) Q1

Video Solution: