Find the component of vector vec{P} = 2 hat{i | vedclass

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

Question

(C) The component of a vector $\vec{P}$ along the direction of another vector $\vec{Q}$ is given by the projection formula: $	ext{Component} = \vec{P

Vedclass · Accepted Answer

$\frac{5}{\sqrt{2}}$

Vedclass · Answer

(C) The component of a vector $\vec{P}$ along the direction of another vector $\vec{Q}$ is given by the projection formula: $	ext{Component} = \vec{P} \cdot \hat{Q} = \vec{P} \cdot \frac{\vec{Q}}{|\vec{Q}|}$.Given $\vec{P} = 2 \hat{i} + 3 \hat{j}$ and $\vec{Q} = \hat{i} + \hat{j}$.First, calculate the magnitude of vector $\vec{Q}$:$|\vec{Q}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Now, calculate the dot product $\vec{P} \cdot \vec{Q}$:$\vec{P} \cdot \vec{Q} = (2 \hat{i} + 3 \hat{j}) \cdot (\hat{i} + \hat{j}) = (2 	imes 1) + (3 	imes 1) = 2 + 3 = 5$.Finally, the component of $\vec{P}$ along $\vec{Q}$ is:$\frac{\vec{P} \cdot \vec{Q}}{|\vec{Q}|} = \frac{5}{\sqrt{2}}$.

Find the component of vector $\vec{P} = 2 \hat{i} + 3 \hat{j}$ along the direction of vector $\vec{Q} = \hat{i} + \hat{j}$.

Similar Questions

If for two vectors $\vec{A}$ and $\vec{B}$,$\vec{A} \times \vec{B} = 0$,then the vectors:

If $a + b + c = 0$,then $a \times b$ is equal to:

If vectors $\vec{A} = (2, -3, 1)$ and $\vec{B} = (3, 4, n)$ are perpendicular to each other,find the value of $n$.

Explain the geometrical interpretation of the scalar product of two vectors.

If $\vec{A} + \vec{B} + \vec{C} = 0$,then $\vec{A} \times \vec{B}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module