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

Answer:

Step-by-step 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. $C+D=2\times \hat{j}+2\hat{i}------2$

From 1 and 2

$2C=3\hat{j}$

$C=1.5\hat{j}$

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