Question

If a straight line $\overline{r}=\overline{a}+\lambda \overline{b}$, meet ,the plane.$\overline{r}\cdot \overline{n}=p$ at, R the position vector of R is given by

• A. $\overline{a}+\left(\frac{\overline{a}.\hat{n}}{\overline{b}.\hat{n}}\right)\overline{b}$
• B. $\overline{a}-\left(\frac{\overline{a}.\hat{n}}{\overline{b}.\hat{n}}\right)\overline{a}$
• C. $\overline{a}-\left(\frac{\overline{a}.\hat{n}}{\overline{b}.\hat{n}}\right)\overline{b}$
• D. None of the above

Answer 1

Answer: (D)

None of the above

Given that the line $r=a+\lambda b$ meets the plane $r.n=p$

By substituting $r=a+\lambda b$ in plane equation , we get $(a+\lambda b).n=p$

$\Rightarrow \lambda =\frac{p-a.n}{b.n}$

The position vector of intersection point is $r=a+\left(\frac{p-a.n}{b.n}\right)b$

Therefore the correct option is $D$