Question

I need help with this problem but just for v

I need to know both it's component form and polar form and<-3,2> is wrong.​

Answer 1

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Answer:

v = <-5, 1> ≈ <5.09902, 168.69°>

Explanation:

Vector u has its tail at the origin, so the coordinates of its head give you the components of the vector. To find the components of vector v, you can translate it so its tail is at the origin, or you can simply subtract the tail coordinates from the head coordinates.

v = <1, -2> -<6, -3> = <1-6, -2-(-3)>

v = <-5, 1>

As you know, the magnitude is the root of the sum of the squares of the components:

|v| = √(5²+1²) = √26 ≈ 5.09902

The tangent of the angle is the ratio of y to x coordinates. When using the arctangent function, the quadrant needs to be taken into account.

∠v = arctan(1/-5) ≈ 168.69°

Vector v is ...

v = <-5, 1> ≈ <5.09902, 168.69°>