The image of the point with position vector $(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})$, in the plane $\mathbf{r} \cdot(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})+3=0$ is

Question

The image of the point with position vector $(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})$, in the plane $\mathbf{r} \cdot(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})+3=0$ is, $(3,5,2)$, $(3,5,-2)$, $(-3,-5,2)$, $(-3,5,2)$

MARKS App · Accepted Answer

Let the image of the point with position vector $(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})$ in the plane $\mathbf{r} \cdot(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})+3=0$ is $\left(x_2, y_2, z_2\right)$, so $\frac{x_2-1}{2}=\frac{y_2-3}{-1}=\frac{z_2-4}{1}=-2 \frac{2-3+4+3}{4+1+1}=-2$ $\Rightarrow \quad x_2=-3, y_2=5 ; z_2=2$ Hence, option (d) is correct.

Search any question & find its solution

Looking for more such questions to practice?