If the vectors vec{AB} = hat{i} + 3hat{j} + 4 | vedclass

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

Question

(A) In a triangle $ABC$,if $A$ is the origin,then the position vectors of $B$ and $C$ are $\vec{AB}$ and $\vec{AC}$ respectively. The position vector

Vedclass · Accepted Answer

$\frac{2}{3} \sqrt{22}$

Vedclass · Answer

(A) In a triangle $ABC$,if $A$ is the origin,then the position vectors of $B$ and $C$ are $\vec{AB}$ and $\vec{AC}$ respectively. The position vector of the centroid $G$ is given by $\vec{AG} = \frac{\vec{AB} + \vec{AC}}{3}$.Substituting the given vectors:$\vec{AG} = \frac{(\hat{i} + 3\hat{j} + 4\hat{k}) + (5\hat{i} + \hat{j} + 2\hat{k})}{3}$$\vec{AG} = \frac{6\hat{i} + 4\hat{j} + 6\hat{k}}{3} = 2\hat{i} + \frac{4}{3}\hat{j} + 2\hat{k}$.Now,calculating the magnitude $|\vec{AG}| = \sqrt{2^2 + (\frac{4}{3})^2 + 2^2} = \sqrt{4 + \frac{16}{9} + 4} = \sqrt{8 + \frac{16}{9}} = \sqrt{\frac{72 + 16}{9}} = \sqrt{\frac{88}{9}} = \frac{\sqrt{4 	imes 22}}{3} = \frac{2}{3}\sqrt{22}$.Thus,the correct option is $(a)$.

If the vectors $\vec{AB} = \hat{i} + 3\hat{j} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} + \hat{j} + 2\hat{k}$ are two sides of a triangle $ABC$,whose centroid is $G$,then $|\vec{AG}| = $

Similar Questions

If $a$ and $b$ are two non-zero and non-collinear vectors,then $a + b$ and $a - b$ are:

The direction cosines of the resultant of the vectors $(i + j + k)$,$(-i + j + k)$,$(i - j + k)$ and $(i + j - k)$ are

If $PQRST$ is a pentagon,then the resultant of forces $\overline{PQ}, \overline{PT}, \overline{QR}, \overline{SR}, \overline{TS}$ and $\overline{PS}$ is

Let $ABCDEF$ be a regular hexagon with the vertices $A, B, C, D, E, F$ in counterclockwise order. Then the vector $\vec{AB} + \vec{AF} + \vec{CD} + \vec{EF}$ is equal to

If the sides of a regular hexagon $ABCDEF$ are given by $\vec{AB} = \bar{a}$ and $\vec{BC} = \bar{b}$,then $\vec{FA} = .....$

Vedclass Test Series

Exam Paper Generator

Online Exam Module