Question

the x and y components of vector A are 4m and 6m respectively. The x and y components of vector A+b are 10m and 9m respectively. for the vector b calculate:
a)x and y components
b)length
c)the angle it makes with x axis

Answer 1

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Answer 2

Answer:  The x and y component of vector B is 6 m and 3 m, the length is $3\sqrt{5} m$ and the angle is $26.6^{\circ}$

Explanation:

Given that,

The x and y components of vector A are 4 m and 6 m and the x and y components of vector A+B = C are 10 m and 9 m.

We have,

$\vec{A}=4\hat{m}+6\hat{m}$

$\vec{C}=10\hat{m}+9\hat{m}$

We know that,

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

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

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

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

(a). x and y component of vector B is 6 m and 3 m.

(b). The length of vector B is

The magnitude of vector B is

$|B|= \sqrt{36+9}$

$|B|=3\sqrt{5} m$

(c). The angle it makes with x axis is

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

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

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

$\theta = 26.6^{\circ}$

Hence, The x and y component of vector B is 6 m and 3 m, the length is $3\sqrt{5} m$ and the angle is $26.6^{\circ}$