If overrightarrow{a}=hat{i}+3 hat{j}+13 hat{k | vedclass

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

Question

(C) The component of vector $\vec{a}$ along $\vec{b}$ is given by $\vec{p} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \right) \vec{b}$.First,c

Vedclass · Accepted Answer

$-\hat{i}+7 \hat{j}+10 \hat{k}$

Vedclass · Answer

(C) The component of vector $\vec{a}$ along $\vec{b}$ is given by $\vec{p} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \right) \vec{b}$.First,calculate the dot product $\vec{a} \cdot \vec{b} = (1)(2) + (3)(-4) + (13)(3) = 2 - 12 + 39 = 29$.Next,calculate the magnitude squared $|\vec{b}|^2 = (2)^2 + (-4)^2 + (3)^2 = 4 + 16 + 9 = 29$.So,the component of $\vec{a}$ along $\vec{b}$ is $\vec{p} = \left( \frac{29}{29} \right) \vec{b} = \vec{b} = 2\hat{i} - 4\hat{j} + 3\hat{k}$.The component of $\vec{a}$ perpendicular to $\vec{b}$ is $\vec{x} = \vec{a} - \vec{p} = \vec{a} - \vec{b}$.$\vec{x} = (\hat{i} + 3\hat{j} + 13\hat{k}) - (2\hat{i} - 4\hat{j} + 3\hat{k}) = (1-2)\hat{i} + (3+4)\hat{j} + (13-3)\hat{k} = -\hat{i} + 7\hat{j} + 10\hat{k}$.

If $\overrightarrow{a}=\hat{i}+3 \hat{j}+13 \hat{k}$ and $\overrightarrow{b}=2 \hat{i}-4 \hat{j}+3 \hat{k}$ are two vectors,then the component vector of $\vec{a}$ perpendicular to $\vec{b}$ is

Similar Questions

Let $\vec{u}, \vec{v}$ and $\vec{w}$ be vectors such that $|\vec{u}+\vec{v}+\vec{w}|=0$. If $|\vec{u}|=3$,$|\vec{v}|=4$ and $|\vec{w}|=5$,then the value of $|\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}|$ is

In a parallelogram $ABCD$,the position vectors of vertices $A$ and $C$ are $3\hat{i} + 3\hat{j} + 5\hat{k}$ and $\hat{i} - 5\hat{j} - 5\hat{k}$ respectively. If $M$ is the midpoint of the diagonal $DB$,find the projection of $\overline{OM}$ on $\overline{OC}$,where $O$ is the origin.

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = x\hat{i} + y\hat{j} + z\hat{k}$,find the number of possible vectors $\vec{b}$ such that $\vec{a} \cdot \vec{b} = 10$,where $(x, y, z) \in \mathbb{N}$.

The projection of vector $\vec{a}$ along vector $\vec{b}$ is:

If $\hat{a}$ is a unit vector such that $(\bar{x}-\hat{a}) \cdot (\bar{x}+\hat{a}) = 8$,then $|\bar{x}| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module