First slide

Vectors

Question

If $A = 3 \hat{i} + 4 \hat{j} and B = 7 \hat{i} + 24 \hat{j}$ the vector having the same magnitude as B and parallel to A is

Moderate

A

$5 \hat{i} + 20 \hat{j}$
B

$15 \hat{i} + 10 \hat{j}$
C

$20 \hat{i} + 15 \hat{j}$
D

$15 \hat{i} + 20 \hat{j}$

Solution

$A ∣ = \sqrt{3^{2} + 4^{2}} = 5$
Desired vector, $r = | B | \hat{A} = (\sqrt{7^{2} + 24^{2}}) \times \frac{3 \hat{i} + 4 \hat{j}}{5} = 15 \hat{i} + 20 \hat{j}$

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