Let overrightarrow{a} and overrightarrow{b} b | vedclass

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

Question

(D) The projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by $\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrighta

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(D) The projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by $\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|}$.The projection of vector $\overrightarrow{b}$ on $\overrightarrow{a}$ is given by $\frac{\overrightarrow{b} \cdot \overrightarrow{a}}{|\overrightarrow{a}|}$.The ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to the projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is:$\frac{\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|}}{\frac{\overrightarrow{b} \cdot \overrightarrow{a}}{|\overrightarrow{a}|}} = \frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|} 	imes \frac{|\overrightarrow{a}|}{\overrightarrow{b} \cdot \overrightarrow{a}}$Since the dot product is commutative,$\overrightarrow{a} \cdot \overrightarrow{b} = \overrightarrow{b} \cdot \overrightarrow{a}$.Therefore,the ratio simplifies to $\frac{|\overrightarrow{a}|}{|\overrightarrow{b}|} = \frac{2}{3}$.

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $|\overrightarrow{a}| = 2$ and $|\overrightarrow{b}| = 3$. Then the ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to that of $\overrightarrow{b}$ on $\overrightarrow{a}$ is:

Similar Questions

The perimeter of a triangle with sides represented by vectors $\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}$,$\vec{b} = 4\hat{i} - 3\hat{j} - 5\hat{k}$,and $\vec{c} = 7\hat{i} + \hat{j}$ is:

$ABCDEF$ is a regular hexagon whose centre is $O$. Then,$\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF}$ is equal to (in $vec{AO}$)

Find the values of $x$ and $y$ so that the vectors $2 \hat{i} + 3 \hat{j}$ and $x \hat{i} + y \hat{j}$ are equal.

Classify the following measure as a scalar or a vector: $20 \, m/s^{2}$.

Show that each of the given three vectors is a unit vector:
$\frac{1}{7}(2 \hat{i}+3 \hat{j}+6 \hat{k}), \frac{1}{7}(3 \hat{i}-6 \hat{j}+2 \hat{k}), \frac{1}{7}(6 \hat{i}+2 \hat{j}-3 \hat{k})$
Also,show that they are mutually perpendicular to each other.

Vedclass Test Series

Exam Paper Generator

Online Exam Module