The direction cosines of the vector 3hat{i} - | vedclass

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

Question

(B) Let the vector be $\vec{A} = 3\hat{i} - 4\hat{j} + 5\hat{k}$.The magnitude of the vector is $|\vec{A}| = \sqrt{3^2 + (-4)^2 + 5^2} = \sqrt{9 + 16

Vedclass · Accepted Answer

$\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{1}{\sqrt{2}}$

Vedclass · Answer

(B) Let the vector be $\vec{A} = 3\hat{i} - 4\hat{j} + 5\hat{k}$.The magnitude of the vector is $|\vec{A}| = \sqrt{3^2 + (-4)^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2}$.The direction cosines $(l, m, n)$ are given by $\frac{x}{|\vec{A}|}, \frac{y}{|\vec{A}|}, \frac{z}{|\vec{A}|}$.Thus,the direction cosines are $\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{5}{5\sqrt{2}}$.Simplifying the third term,$\frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}$.Therefore,the direction cosines are $\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{1}{\sqrt{2}}$.

The direction cosines of the vector $3\hat{i} - 4\hat{j} + 5\hat{k}$ are

Similar Questions

Find a unit vector in the direction of $\overrightarrow{PQ},$ where $P$ and $Q$ have coordinates $(5, 0, 8)$ and $(3, 3, 2),$ respectively.

In $\triangle ABC$,$L, M, N$ are points on $BC, CA, AB$ respectively,dividing them in the ratio $1:2, 2:3, 3:5$. If the point $K$ divides $AB$ in the ratio $5:3$,then find the value of $\left| \frac{\vec{AL} + \vec{BM} + \vec{CN}}{\vec{CK}} \right|$.

The vertices of triangle $ABC$ are $A \equiv (3, 0, 0)$,$B \equiv (0, 0, 4)$,and $C \equiv (0, 5, 4)$. Find the position vector of the point $D$ where the angle bisector of $\angle A$ meets $BC$.

If $\vec{a} = \vec{b}$,then............

Vedclass Test Series

Exam Paper Generator

Online Exam Module