Find the sum of the vectors vec{a}=hat{i}-2 h | vedclass

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

Question

(A) Given vectors are $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.The sum o

Vedclass · Accepted Answer

$-4\hat{j}-\hat{k}$

Vedclass · Answer

(A) Given vectors are $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.The sum of the vectors is given by $\vec{a} + \vec{b} + \vec{c} = (\vec{a}_x + \vec{b}_x + \vec{c}_x)\hat{i} + (\vec{a}_y + \vec{b}_y + \vec{c}_y)\hat{j} + (\vec{a}_z + \vec{b}_z + \vec{c}_z)\hat{k}$.Substituting the components:$\vec{a} + \vec{b} + \vec{c} = (1 - 2 + 1)\hat{i} + (-2 + 4 - 6)\hat{j} + (1 + 5 - 7)\hat{k}$.Calculating the coefficients:$x$-component: $1 - 2 + 1 = 0$.$y$-component: $-2 + 4 - 6 = -4$.$z$-component: $1 + 5 - 7 = -1$.Thus,the sum is $0\hat{i} - 4\hat{j} - 1\hat{k} = -4\hat{j} - \hat{k}$.

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 $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

Similar Questions

$a, b, c$ are non-coplanar vectors. If $a+3 b+4 c=x(a-2 b+3 c)+y(a+5 b-2 c)+z(6 a+14 b+4 c)$,then $x+y+z=$

If $\bar{a}$ and $\bar{b}$ are two non-parallel unit vectors and the vector $\alpha \bar{a} + \bar{b}$ bisects the internal angle between $\bar{a}$ and $\bar{b}$,then $\alpha$ is equal to

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

Write all the unit vectors in the $XY$-plane.

Let $ABC$ be a triangle. Let $u = \vec{AB}$ and $v = \vec{AC}$. If $D$ is the midpoint of $BC$,then $\vec{AD} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module