Three vectors vec{a}, vec{b}, vec{c} satisfy | vedclass

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

Question

(C) Given that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$.Squaring both sides,we get $(\vec{a}+\vec{b}+\vec{c}) \cdot (\vec{a}+\vec{b}+\vec{c}) = \vec{0} \cdot

Vedclass · Accepted Answer

$-13$

Vedclass · Answer

(C) Given that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$.Squaring both sides,we get $(\vec{a}+\vec{b}+\vec{c}) \cdot (\vec{a}+\vec{b}+\vec{c}) = \vec{0} \cdot \vec{0}$.This expands to $|\vec{a}|^2+|\vec{b}|^2+|\vec{c}|^2+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) = 0$.Substituting the given magnitudes $|\vec{a}|=1, |\vec{b}|=3, |\vec{c}|=4$:$(1)^2+(3)^2+(4)^2+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) = 0$.$1+9+16+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) = 0$.$26+2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) = 0$.$2(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}) = -26$.Therefore,$\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} = -13$.

Three vectors $\vec{a}, \vec{b}, \vec{c}$ satisfy the condition $\vec{a}+\vec{b}+\vec{c}=\vec{0}$. If $|\vec{a}|=1, |\vec{b}|=3, |\vec{c}|=4$,then find the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}$.

Similar Questions

If $a$ and $b$ are unit vectors such that $a+b$ is also a unit vector,then the angle between $a$ and $b$ is . . . . . . (in $^{\circ}$)

Let $\bar{a} = 2\hat{i} + \hat{j} + \hat{k}$,$\bar{b} = \hat{i} + 2\hat{j} - \hat{k}$,and vector $\bar{c}$ be coplanar with $\bar{a}$ and $\bar{b}$. If $\bar{c}$ is perpendicular to $\bar{a}$,then $\bar{c}$ is:

The orthogonal projection of vector $a$ on vector $b$ is given by:

If $\bar{a}=2 \hat{i}+2 \hat{j}+3 \hat{k}$,$\bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ are vectors such that $\bar{a}+\lambda \bar{b}$ is perpendicular to $\bar{c}$,then the value of $\lambda$ is

If the vectors $3i + 2j + 8k$ and $2i + xj + k$ are perpendicular to each other,then $x = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module