Q93 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics

If $\mathbf{p} \times \mathbf{q}=\mathbf{p} \times \mathbf{r}$ and $\mathbf{p} \cdot \mathbf{q}=\mathbf{p} \cdot \mathbf{r}$, then $\ldots . . .$.

  • A
    $p=r$
  • Correct answer
    B
    $q=r$
  • C
    $p=q$
  • D
    $p+q=0$

Solution

$\mathbf{p} \times \mathbf{q}=\mathbf{p} \times \mathbf{r}$ $$ \begin{aligned} & \Rightarrow \quad \mathbf{p} \times(\mathbf{q}-\mathbf{r})=0 \\ & \text { p.q }=\text { p. } r \\ & \Rightarrow \quad \text { p. }(\mathbf{q}-\mathbf{r})=0 \\ & \end{aligned} $$ From Eqs. (i) and (ii) we can say that $\mathbf{p}$ is neither parallel nor Perpendicular to $(\mathbf{q}-\mathbf{r})$ $$ \begin{aligned} & \Rightarrow \quad \mathbf{q}-\mathbf{r}=0 \\ & {[\because \mathbf{p} \neq 0]} \\ & \Rightarrow \quad \mathbf{q}=\mathbf{r} \\ & \end{aligned} $$ Hence, option (2) is correct.

Hence, the correct answer is option: 'B'.

Relevant Questions