The angle between the lines whose direction r | vedclass

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

Question

(A) Let the two direction vectors be $\vec{v_1} = a\hat{i} + b\hat{j} + c\hat{k}$ and $\vec{v_2} = (b-c)\hat{i} + (c-a)\hat{j} + (a-b)\hat{k}$.Calcula

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) Let the two direction vectors be $\vec{v_1} = a\hat{i} + b\hat{j} + c\hat{k}$ and $\vec{v_2} = (b-c)\hat{i} + (c-a)\hat{j} + (a-b)\hat{k}$.Calculate the dot product $\vec{v_1} \cdot \vec{v_2} = a(b-c) + b(c-a) + c(a-b)$.Expand the terms: $ab - ac + bc - ba + ca - cb$.Simplify the expression: $(ab - ba) + (bc - cb) + (ca - ac) = 0 + 0 + 0 = 0$.Since the dot product is $0$, the vectors are perpendicular, and the angle between the lines is $90^\circ$.

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is (in $^\circ$)

Similar Questions

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is

The angle between the lines,whose direction cosines $l, m, n$ satisfy the equations $l+m+n=0$ and $2l^2+2m^2-n^2=0$,is (in $^{\circ}$)

The coordinates of a point $P$ are $(3, 12, 4)$ with respect to origin $O$. Find the direction cosines of $OP$.

$A$ point is in the $XZ-$ plane. What can you say about its $y-$ coordinate?

If the direction ratios of two lines are given by $a+2b+c=0$ and $11bc+6ca-14ab=0$, then the angle between these lines is

Vedclass Test Series

Exam Paper Generator

Online Exam Module