First slide

Vectors

Question

The magnitude of the x-component of vector $\vec{A}$ is 3 and the magnitude of vector $\vec{A}$ is 5. What is the magnitude of the y-component of vector $\vec{A}$ ?

Moderate

A

3
B

4
C

5
D

8

Solution

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j}$
Also, A = $\sqrt{A_{x}^{2} + A_{y}^{2}}$
$∴ 5 = \sqrt{{(3)}^{2} + A_{y}^{2}}$
Squaring both side, we get $25 = 9 + A_{y}^{2}$
$A_{y}^{2} = 25 - 9 = 16 or A_{y} = 4$

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