Question

Write the vector v in the form aiplusbj​, given its magnitude left norm Bold v right norm and the angle alpha it makes with the positive​ x-axis.Left norm Bold v right normequals12​, alphaequals150

Answer 1

`6√(3)i-6j`

Explanation:

Given:

The magnitude, v=12

The angle
`\alpha` it makes with the positive​ x-axis =
`150^0`

Now for a vector (x,y)

• 
  `\alpha =tan^(-1)((y)/(x) )` ; and

• 
  `v=√(x^2+y^2)`

Therefore:

`150 =tan^(-1)((y)/(x) )\\(y)/(x) =tan 150\\(y)/(x)=-(√(3) )/(3)`

`y=-(x √(3))/(3)`

Similarly:

`v=√(x^2+y^2)\\12=√(x^2+y^2)\\12^2=x^2+y^2\\144=x^2+y^2`

`144=x^2+(-(x √(3))/(3) )^2\\144=x^2+(3x^2)/(9) \\144=(4x^2)/(3)\\4x^2=144 X 3=432\\x^2=108\\x=6√(3)`

Recall that:

`y=-(x √(3))/(3)\\y=-(6√(3) √(3))/(3)=-6`

Therefore:
`(x,y)=(6√(3), -6)`

The vector in the form ai+bj is therefore:

`6√(3)i-6j`