Question

Consider the three dip1acement vectors A = (3i - 3j) m, B = (i-4j) m, and C = (-2i + 5j) m. Use the component method to determine (a) the magnitude and direction of the vector + + and (b) the magnitude and direction of E=-A - B + C.

Answer 1

Answer with Explanation:

We are given that

A=3i-3j m

B=i-4 j m

C=-2i+5j m

a.
`D=A+B+C`

`D=3i-3j+i-4j-2i+5j`

`D=2i-2j`

Compare with the vector r=xi+yj

We get x=2 and y=-2

Magnitude=
`\mid D\mid=√(x^2+y^2)=√((2)^2+(-2)^2)=2\sqrt 2` units

By using the formula
`\mid r\mid=√(x^2+y^2)`

Direction:
`\theta=tan^(-1)(y)/(x)`

By using the formula

Direction of D:
`\theta=tan^(-1)((-2)/(2))=tan^(-1)(-1)=tan^(-1)(-tan45^(\circ))=-45^(\circ)`

b.E=-A-B+C

`E=-3i+3j-i+4j-2i+5j`

`E=-6i+12j`

`\mid E\mid=√((-6)^2+(12)^2)=13.4`units

Direction of E=
`\theta=tan^(-1)((12)/(-6)=tan^(-1)(-2)=-63.4^(\circ)`