Question

For component of vector $\overrightarrow{P}=\hat{i}+2\hat{j}-3\hat{k}$ values are in column - II, then the correct match is:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{a)}& \text{X-axis}& \text{p)}& 1\\ \text{b)}& \text{Along vector}& \text{q)}& \sqrt{14}\\ & \overrightarrow{q}=\hat{i}+2\hat{j}+\frac{5}{3}\hat{k}& & \\ \text{c)}& \text{Along vector}& \text{r)}& 0\\ & \overrightarrow{r}=2\hat{i}+4\hat{j}-6\hat{k}& & \\ \text{d)}& \text{Along vector}& \text{s)}& \sqrt{7}\\ & \overrightarrow{s}=\frac{\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{14}}& & \end{array}$

• A. $a\to s,b\to q,c\to r,d\to q$
• B. $a\to p,b\to r,c\to q,d\to q$
• C. $a\to p,b\to r,c\to s,d\to q$
• D. $a\to p,b\to q,c\to r,d\to s$

Answer 1

The correct option is B $a\to p,b\to r,c\to q,d\to q$

a) Along $x-$ axis it is $1$
b) Since $\overrightarrow{p}.\overrightarrow{q}=0$
c) $\overrightarrow{r}$ is parallel to $\overrightarrow{p}$
d) $\overrightarrow{s}$ is unit vector in the direction of $\overrightarrow{p}$