The projection of vector vec A on vector vec | vedclass

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

Question

(B) The projection of a vector $\vec A$ onto a vector $\vec B$ is defined as the scalar component of $\vec A$ in the direction of $\vec B$.Mathematica

Vedclass · Accepted Answer

$\vec A \cdot \hat B$

Vedclass · Answer

(B) The projection of a vector $\vec A$ onto a vector $\vec B$ is defined as the scalar component of $\vec A$ in the direction of $\vec B$.Mathematically,this is given by the dot product of $\vec A$ with the unit vector of $\vec B$.Projection $= |\vec A| \cos 	heta$.Since $\vec A \cdot \vec B = |\vec A| |\vec B| \cos 	heta$,we have $|\vec A| \cos 	heta = \frac{\vec A \cdot \vec B}{|\vec B|}$.Since the unit vector $\hat B = \frac{\vec B}{|\vec B|}$,the projection is $\vec A \cdot \hat B$.

The projection of vector $\vec A$ on vector $\vec B$ is:

Similar Questions

The two vectors have magnitudes $3$ and $5$. If the angle between them is $60^o$,then the dot product of the two vectors will be:

Given $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,find the unit vector perpendicular to both.

Two forces $\vec F_1 = 5\hat i + 10\hat j - 20\hat k$ and $\vec F_2 = 10\hat i - 5\hat j - 15\hat k$ act on a single point. The angle between $\vec F_1$ and $\vec F_2$ is nearly . . . . . . $^\circ$.

The angle between the vectors $(\hat{i} + \hat{j})$ and $(\hat{i} - \hat{k})$ is ........ $^\circ$.

$\hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module