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Precalculus

Course: Precalculus > Unit 6

Lesson 7: Vector components from magnitude and direction
Math
Precalculus
Vectors
Vector components from magnitude and direction
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Vector components from magnitude & direction (advanced)

Google Classroom
Find a vector's components from its magnitude and direction. Direction angle is not given directly.

Introduction

Each of the two problems below asks you to convert a vector from magnitude and direction form into component form.
But watch out! The direction angles aren't given for these vectors. You'll need to be careful what you plug into the sine and cosine functions.

Problem 1

The vector v, with, vector, on top is shown below.
Find the component form of v, with, vector, on top.
Round your final answers to the nearest hundredth.
v, with, vector, on top, approximately equals, left parenthesis, space
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
space, comma
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
right parenthesis, space

Problem 2

The vector u, with, vector, on top is shown below.
What is the component form of u, with, vector, on top?
Round your final answer to the nearest hundredth.
u, with, vector, on top, approximately equals, left parenthesis, space
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
space, comma
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
right parenthesis, space

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