Question

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

• A. $\frac{3}{2}\left(\vec {i}+\vec {j}\right)$
• B. $\frac{2}{3}\left(\vec{i}+\vec{j}\right)$
• C. $\frac{1}{2}\left(\vec {i}+\vec{j}\right)$
• D. $\frac{1}{3}\left(\vec {i}+\vec {j}\right)$

Answer 1

Answer: (A)

$\frac{3}{2}\left(\vec {i}+\vec {j}\right)$

Answer 2

Since, $b _{1} \| a$, therefore $b _{1}-a( i + j )$
$b _{2}= b - b _{1}=(3-a) i -a j +4 k$
Also, $b _{2} \cdot a =0$
$\Rightarrow (3-a)-a \Rightarrow a=\frac{3}{2}$
Hence, $b _{1}=\frac{3}{2}( i + j )$