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)

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

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

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