Question

If vector C is added to vector D, the result is a third vector that is perpendicular to D and has a magnitude equal to 3D. What is the ratio of the magnitude of C to that of D?
a) 1.3
b) 1.6
c) 1.8
d) 2.2
e) 3.2

Answer 1

Answer:

(e) 3.2

Explanation:

We are given that vector C and D.

Let R be the magnitude of C+D.

According to question

R=3D

We have to find the ratio of the magnitude of C to that of D.

By using right triangle property

$C^2=R^2+D^2$

$C^2=(3D)^2+D^2$

$C^2=9D^2+D^2$

$C^2=10D^2$

$C=\sqrt{10D^2}=3.2D$

$\frac{C}{D}=3.2$

Hence, the ratio of the magnitude of C to that of D=3.2

(e) 3.2