Question

Two vectors are given by $\vec{A} = (\hat{i} + 2j + \hat{k})$ and $\vec{B} = (3\hat{i} + 6\hat{j} + 2\hat{k})$. Another vector $\vec{C}$ has the same magnitude as $\vec{B}$ but has the same direction as $\vec{A}$. Then which of the following vectors represents $\vec{C}$ ?

• A. $\frac{7}{3}\left( \hat{i} + 2\hat{j} + 2\hat{k}\right)$
• B. $\frac{3}{7}\left( \hat{i} - 2\hat{j} + 2\hat{k}\right)$
• C. $\frac{7}{9}\left( \hat{i} - 2\hat{j} + 2\hat{k}\right)$
• D. $\frac{9}{7}\left( \hat{i} + 2\hat{j} + 2\hat{k}\right)$

Answer 1

Answer: (A)

$\frac{7}{3}\left( \hat{i} + 2\hat{j} + 2\hat{k}\right)$

Answer 2

Given, $A=\hat{i}+2 \hat{ j }+2 \hat{ k }$ and $B =3 \hat{ i }+6 \hat{ j }+2 \hat{ k }$
So, $C =\frac{\hat{ i }+2 \hat{ j }+2 \hat{ k }}{\sqrt{1+4+4}} \times \sqrt{3^{2}+6^{2}+2^{2}}$
$=\frac{\hat{ i }+2 \hat{ j }+2 \hat{ k }}{3} \times \sqrt{49}=\frac{7}{3}(\hat{i}+2 \hat{ j }+2 \hat{ k })$