First slide

Vectors

Question

If a vector A having a magnitude of 8 is added to a vector B which lies along X-axis, then the resultant of
two vectors lies along Y-axis and has magnitude twice that of B, The magnitude of B is

Moderate

A

$\frac{6}{\sqrt{5}}$
B

$\frac{12}{\sqrt{5}}$
C

$\frac{16}{\sqrt{5}}$
D

$\frac{8}{\sqrt{5}}$

Solution

According to given condition,
A+ B $\hat{i}$ = R $\hat{j}$ (where, R is the resultant vector)
Also, R = 2B
$∴ ∣ A + B \hat{i} = 2 B \hat{j} or A = 2 B \hat{j} - B \hat{i}$
$∴$ A² = 4B² + B² = 5B²
Here, A = 8
$∴$ 64 = 5B²
$\Rightarrow B = \sqrt{\frac{64}{5}} = \frac{8}{\sqrt{5}}$

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