Question

If A represents a vector two units in length directed due west, B represents a vector three units in length directed due north and A+B=C-D and 2B-A=C+D.

find the magnitudes and directions ofC and D.

Answer 1

Explanation:

Given

Vector A has two units in length due to west i.e.

`\vec{A}=-2\hat{i}`

Vector B has one unit in length due to North i.e.

`\vec{B}=\hat{j}`

Also
`A+B=C-D`

i.e.
`C-D=-2\hat{i}+\hat{j}--------1`

also
`2B-A=C+D`

i.e.
`C+D=2* \hat{j}+2\hat{i}------2`

From 1 and 2

`2C=3\hat{j}`

`C=1.5\hat{j}`

`D=2\hat{i}+0.5\hat{j}`