Write a vector normal to the plane r =l b +m c . - Vidyadip

Question

Write a vector normal to the plane $\vec{\text{r}}=\text{l}\vec{\text{b}}+\text{m}\vec{\text{c}}$ .

✓

Answer

The equation of the given plane is
$\vec{\text{r}}=\text{l}\vec{\text{b}}+\text{m}\vec{\text{c}}$
So, the plane passes parallel to the vectors $\vec{\text{b}}$ and $\vec{\text{c}}$.
So, the vector normal to the plane is $\vec{\text{b}}\times\vec{\text{c}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Give example of matrices:
A and B such that AB = 0 but BA ≠ 0

Find the area of the region bounded by the curve $y^2=9 x, x=2, x=4$ and the $x-$axis in the first quadrant.

Find the general solution of the differential equation $\frac{d y}{d x}+y=1~(y \neq 1)$

Verify that the function $x + y = \tan^{-1}y$ (explicit or implicit) is a solution of differential equation $y^2y' + y^2 + 1 = 0$.

Differentiate the functions with respect to x.
$\cos(\sqrt{\text{x})}$

If $y=\sqrt{\sin x+y}$, then find $\frac{d y}{d x}$.

For what value of $\lambda$ is the function $\text{f(x)}=\begin{cases}\lambda(\text{x}^2-2\text{x}),&\text{if }\text{ x}\leq0\\4\text{x}+1,&\text{if }\text{ x}>0\end{cases}$ continuous at x = 0? What about continuity at $\text{x}=\pm1?$

If $\text{A}=\begin{bmatrix}0&-1&2\\4&3&-4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}4&0\\1&3\\2&6\end{bmatrix},$ then verify that $(\text{A}')'=\text{A}.$

Evalute the following integrals:
$\int\frac{\text{x}+1}{\text{x}(\text{x}+\log\text{x})}\text{dx}$

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
not more than one.