Question

The x and y-components of vectors A are 4 m and 6 m respectively. The x and y-components of vector A + B are 10 m and 9 m respectively. Calculate for the vector B the following:
A) its x and y-components
B) length
C) the angle it makes with x-axis

Answer 1

Answer: x and y component is 6 and 3, the length is 6.71 m and angle is the $\theta = 26.5^{\circ}$.

Explanation:

Given that,

x and y components of vectors A = 4 m and 6 m

$\vec{A}= 4\hat{i}+6\hat{j}$

x and y components of vectors A+B = 10 m and 9 m

A+B = $\vec{C}= 10\hat{i}+9\hat{j}$

We know that,

$\vec{A}+\vec{B}=\vec{C}$

Where,

$\vec{C}$=the resultant vector of A and B

$\vec{B}= 10\hat{i}+9\hat{j} -4\hat{i}-6\hat{j}$

$\vec{B}= 6\hat{i}+3\hat{j}$

(I). its x and y components is

$x = 6$ and $y = 3$

(II). The magnitude of vector B is

$B = \sqrt{6^2+3^2}$

$B = 6.71\ m$

This is the length.

(III). The angle it makes with x-axis will be

$\tan\theta = \dfrac{y}{x}$

$\tan\theta = \dfrac{3}{6}$

$\tan\theta = \dfrac{1}{2}$

$\theta = \tan^{-1}\dfrac{1}{2}$

$\theta = 26.5^{\circ}$

Hence, This is the required solution.

Answer 2

Answer:

here is your answer dear .......