The angle between the planes 2x - y + z = 6 a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The equation of the first plane is $2x - y + z = 6$,so its normal vector is $\vec{n_1} = 2\hat{i} - \hat{j} + \hat{k}$.The equation of the second

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(D) The equation of the first plane is $2x - y + z = 6$,so its normal vector is $\vec{n_1} = 2\hat{i} - \hat{j} + \hat{k}$.The equation of the second plane is $x + y + 2z = 7$,so its normal vector is $\vec{n_2} = \hat{i} + \hat{j} + 2\hat{k}$.The angle $	heta$ between two planes is given by $\cos 	heta = \frac{|\vec{n_1} \cdot \vec{n_2}|}{|\vec{n_1}| |\vec{n_2}|}$.Calculating the dot product: $\vec{n_1} \cdot \vec{n_2} = (2)(1) + (-1)(1) + (1)(2) = 2 - 1 + 2 = 3$.Calculating the magnitudes: $|\vec{n_1}| = \sqrt{2^2 + (-1)^2 + 1^2} = \sqrt{4 + 1 + 1} = \sqrt{6}$ and $|\vec{n_2}| = \sqrt{1^2 + 1^2 + 2^2} = \sqrt{1 + 1 + 4} = \sqrt{6}$.Thus,$\cos 	heta = \frac{3}{\sqrt{6} \cdot \sqrt{6}} = \frac{3}{6} = \frac{1}{2}$.Therefore,$	heta = \cos^{-1}(\frac{1}{2}) = 60^o$.

The angle between the planes $2x - y + z = 6$ and $x + y + 2z = 7$ is ......... $^o$

Similar Questions

The equations $|x| = p, |y| = p, |z| = p$ in $xyz$ space represent:

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is

If $O$ is the origin and the coordinates of $P$ are $(1, 2, -3)$,then the equation of the plane passing through $P$ and perpendicular to $OP$ is

The foot of the perpendicular drawn from the point $(-2,-1,3)$ to a plane $\pi$ is $(1,0,-2)$. If $a, b, c$ are the intercepts made by the plane $\pi$ on $X, Y, Z$-axes respectively, then $3a+b+5c=$

The foot of the perpendicular from the origin $O$ to a plane $P$,which meets the coordinate axes at points $A, B, C$,is $(2, a, 4)$,where $a \in N$. If the volume of the tetrahedron $OABC$ is $144 \text{ unit}^3$,then which of the following points does $NOT$ lie on the plane $P$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module