Question

Type the correct answer in each box. Round your answers to two decimal places.
Subtract vector v = <2, -3> from vector u = <5, 2>.
The magnitude of the resulting vector, u - v, is approximately __
and its angle of direction is approximately ___

Answer 1

The magnitude of the resulting vector, u - v, is approximately 5.83

and its angle of direction is approximately 59.04°.

How to find the magnitude of the resulting vector?

We want to subtract vector v from vector u.

We are given;

v = <2, -3> = 2i - 3j

u = <5, 2> = 5i + 2j

u - v = 5i + 2j - (2i - 3j)

= 5i + 2j - 2i + 3j

= 3i + 5j

Resultant vector = √(3² + 5²)

Resultant vector = √34 ≈ 5.83

Angle of direction of resultant vector is;

tan θ = (5/3)

θ = tan⁻¹(5/3)

θ = 59.04°

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