Answer to Question #350074 in Analytic Geometry for REED

Question

Given that a = 3i - 5j, determine the angle vector a makes with the positive x-axis b. Given that c = 5i + 3j, d = 3i – 2j. Find the magnitude of (i) c + d (ii) c – d

Answer 1

a.

$\tan\theta=\dfrac{-5}{3}$

Quadrant IV

$\theta=360\degree-\tan^{-1}\dfrac{5}{3}\approx301\degree$

The acute angle which a vector makes with the positive x-axis is $59\degree$ clockwise.

b.

(i)

$\vec{c}+\vec{d}=(5+3)\vec{i}+(3-2)\vec{j}$

$=8\vec{i}+\vec{j}$

$|\vec{c}+\vec{d}|=\sqrt{(8)^2+(1)^2}=\sqrt{82}$

(ii)

$\vec{c}-\vec{d}=(5-3)\vec{i}+(3-(-2))\vec{j}$

$=2\vec{i}+5\vec{j}$

$|\vec{c}-\vec{d}|=\sqrt{(2)^2+(5)^2}=\sqrt{29}$