Question

Given vector A = 2i + 3j and vector B = i + j. What is the vector component of A in the direction of B?

Answer 1

Answer: The vector component of A in the direction of B is $A\cos\theta= \dfrac{5}{\sqrt{2}}$.

Explanation:

Given that,

Vector A = $2\hat{i}+3\hat{j}$

Vector B = $\hat{i}+\hat{j}$

We know that,

The vector component of A in the direction of B is

$\vec{A}\cdot\vec{B}=|A||B|cos\theta$

$A\cos\theta=\dfrac{\vec{A}\cdot \vec{B}}{|B|}$

$A\cos\theta=\dfrac{2\hat{i}+3\hat{j}\cdot\hat{i}+\hat{j}}{\sqrt{2}}$

$A\cos\theta= \dfrac{5}{\sqrt{2}}$

Hence, The vector component of A in the direction of B is $A\cos\theta= \dfrac{5}{\sqrt{2}}$.

Answer 2

The vector component of A in the direction of B is, $A \cos \theta=\frac{5}{\sqrt{2}}$

What is vector components?

• Components Of A Vector.
• The components of a vector in two dimension coordinate system are usually considered to be x-component and y-component.
• It can be represented as, V = (vx, vy), where V is the vector.
• These are the parts of vectors generated along the axes.

What are vector quantities?

• The physical quantities for which both magnitude and direction are defined distinctly are known as vector quantities.
• For example, a boy is riding a bike with a velocity of 30 km/hr in a north-east direction.

According to the question:

Given that,

Vector $\mathrm{A}=2 \hat{i}+3 \hat{j}$

Vector $\mathrm{B}=\hat{i}+\hat{j}$

We know that,

The vector component of A in the direction of B is

$\vec{A} \cdot \vec{B}=|A||B| \cos \theta A \cos \theta=\frac{\vec{A} \cdot \vec{B}}{|B|} \\\\ A \cos \theta=\frac{2 \hat{i}+3 \hat{j} \cdot \hat{i}+\hat{j}}{\sqrt{2}} \\\\ A \cos \theta=\frac{5}{\sqrt{2}}$

Hence, The vector component of $\mathbf{A}$ in the direction of $\mathbf{B}$ is,

$A \cos \theta=\frac{5}{\sqrt{2}} .$

Hence, The vector component of A in the direction of B is, $A \cos \theta=\frac{5}{\sqrt{2}}$

Learn more about vector component here,

https://brainly.in/question/18481525?msp_poc_exp=5

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