Question

Consider the three displacement vectors

A=(3i+3j)meters,
B-(i-4j) m
C=(-2i+5j) m
Use the Component method to determine
a) the magnitude and direction of the vector D= A+B+C
b) the magnitude And direction of E=-A-B+C

Answer 1

Step-by-step explanation:

`\overrightarrow{A} = 3\widehat{i}+3\widehat{j}`

`\overrightarrow{B} = \widehat{i}-4\widehat{j}`

`\overrightarrow{C} = -2\widehat{i}+5\widehat{j}`

(a)

`\overrightarrow{D} =\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}`

`\overrightarrow{D} =\left ( 3+1-2 \right )\widehat{i} +\left ( 3-4+5 \right )\widehat{j}`

`\overrightarrow{D} =\left 2\widehat{i} +4\widehat{j}`

Magnitude of
`\overrightarrow{D}` =
`\sqrt{2^(2)+4^(2)}`

= 4.47 m

Let θ be the direction of vector D

`tan\theta =(4)/(2)`

θ = 63.44°

(b)

`\overrightarrow{E} = </p><p>- \overrightarrow{A}-\overrightarrow{B}+\overrightarrow{C}`

`\overrightarrow{E} =\left ( - 3- 1 -2 \right )\widehat{i} +\left ( - 3 + 4+5 \right )\widehat{j}`

`\overrightarrow{E} =- \left 6\widehat{i} +6\widehat{j}`

Magnitude of
`\overrightarrow{E}` =
`\sqrt{6^(2)+6^(2)}`

= 8.485 m

Let θ be the direction of vector D

`tan\theta =(6)/(-6)`

θ = 135°