The angle between the lines x=y, z=0 and y=0, | vedclass

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

Question

(B) The first line is given by $x=y$ and $z=0$. This line lies in the $xy$-plane. Its direction vector $\vec{v_1}$ can be written as $(1, 1, 0)$.The s

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(B) The first line is given by $x=y$ and $z=0$. This line lies in the $xy$-plane. Its direction vector $\vec{v_1}$ can be written as $(1, 1, 0)$.The second line is given by $y=0$ and $z=0$. This is the $x$-axis. Its direction vector $\vec{v_2}$ is $(1, 0, 0)$.The angle $	heta$ between two lines with direction vectors $\vec{v_1}$ and $\vec{v_2}$ is given by $\cos 	heta = \frac{|\vec{v_1} \cdot \vec{v_2}|}{|\vec{v_1}| |\vec{v_2}|}$.Calculating the dot product: $\vec{v_1} \cdot \vec{v_2} = (1)(1) + (1)(0) + (0)(0) = 1$.Calculating the magnitudes: $|\vec{v_1}| = \sqrt{1^2 + 1^2 + 0^2} = \sqrt{2}$ and $|\vec{v_2}| = \sqrt{1^2 + 0^2 + 0^2} = 1$.Substituting these values: $\cos 	heta = \frac{1}{\sqrt{2} 	imes 1} = \frac{1}{\sqrt{2}}$.Therefore,$	heta = 45^{\circ}$.

The angle between the lines $x=y, z=0$ and $y=0, z=0$ is (in $^{\circ}$)

Similar Questions

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\lambda}{2}=\frac{z}{1}$ intersect each other,then $\lambda = \ldots$

If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar,then the value of $k$ is $.....$

If $A(1, 2, 1)$,$B(2, 3, 2)$,$C(2, 1, 3)$,and $D(3, 2, 4)$,then which of the following is true?

The vector equation of the line joining the points $i - 2j + k$ and $-2j + 3k$ is

Find the position vector of the image of the point with position vector $\vec{P} = 2\hat{i} + \hat{j} + 3\hat{k}$ in the line whose vector equation is $\vec{r} = \hat{j} - 2\hat{k} + \lambda(\hat{i} + \hat{j} - \hat{k})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module