Question

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

• A. $5\widehat{i} + 20\widehat{j}$
• B. $15\widehat{i} + 10\widehat{j}$
• C. $20\widehat{i} + 15\widehat{j}$
• D. $15\widehat{i} + 20\widehat{j}$

Answer 1

Answer: (D)

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

Answer 2

$|B| = \sqrt{7^{2} + (24)^{2}}$ $= \sqrt{625}$ $= 25$

Unit vector in the direction of A will be

$\widehat{A} = \frac{3\widehat{i} + 4\widehat{j}}{5}$

So required vector

=$25\left( \frac{3\widehat{i} + 4\widehat{j}}{5} \right)$ $= 15\widehat{i} + 20\widehat{j}$