Let the vectors overrightarrow{AB} = 2hat{i} | vedclass

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

Question

(B) Given vectors are $\overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k}$.Let the positio

Vedclass · Accepted Answer

$38$

Vedclass · Answer

(B) Given vectors are $\overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k}$.Let the position vector of $A$ be $\vec{0}$. Then the position vectors of $B$ and $C$ are $\vec{B} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{C} = 2\hat{i} + 4\hat{j} + 4\hat{k}$.The centroid $G$ of $	riangle ABC$ has the position vector $\overrightarrow{AG} = \frac{\vec{A} + \vec{B} + \vec{C}}{3} = \frac{\vec{0} + (2\hat{i} + 2\hat{j} + \hat{k}) + (2\hat{i} + 4\hat{j} + 4\hat{k})}{3} = \frac{4\hat{i} + 6\hat{j} + 5\hat{k}}{3}$.Now,calculate the square of the magnitude $|\overrightarrow{AG}|^2 = \left(\frac{4}{3}ight)^2 + \left(\frac{6}{3}ight)^2 + \left(\frac{5}{3}ight)^2 = \frac{16 + 36 + 25}{9} = \frac{77}{9}$.Substitute this into the expression: $\frac{27}{7}(\overrightarrow{AG})^2 + 5 = \frac{27}{7} 	imes \frac{77}{9} + 5 = 3 	imes 11 + 5 = 33 + 5 = 38$.Thus,the correct option is $B$.

Let the vectors $\overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ be two sides of a triangle $ABC$. If $G$ is the centroid of $\triangle ABC$,then $\frac{27}{7}(\overrightarrow{AG})^2 + 5 =$

Similar Questions

Answer the following as true or false.
Two collinear vectors having the same magnitude are equal.

Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the midpoints of the diagonals $AC$ and $BD$ respectively and $(\overrightarrow{AB}-\overrightarrow{BC})+(\overrightarrow{AD}-\overrightarrow{DC})= k \overrightarrow{FE}$,then $k$ is equal to

The projections of a vector on the three coordinate axes are $6, -3, 2$ respectively. The direction cosines of the vector are:

Let $A, B, C$ be distinct points with position vectors $\hat{i} + \hat{j}$,$\hat{i} - \hat{j}$,and $p\hat{i} - q\hat{j} + r\hat{k}$ respectively. If points $A, B, C$ are collinear,then which of the following can be correct?

Find the sum of the vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module