IXL - Find the magnitude and direction of a vector sum (Precalculus practice)

The vector

has magnitude 7 and direction angle

The vector

has magnitude 3 and direction angle

Find the magnitude and direction angle

of the sum

Round your answers to the nearest thousandth.

ref_doc_title.

Learn with an example

question

The vector

has magnitude 4 and direction angle

The vector

has magnitude 7 and direction angle

Find the magnitude and direction angle

of the sum

Round your answers to the nearest thousandth.

key idea

solution

Find the components of

and

When a vector's direction angle is a multiple of

you can easily find its components by graphing it in the coordinate plane.

The vector

has direction angle

so it lies on the positive

-axis

when its initial point is the origin. Since

the distance from the initial point of

to its terminal point is 4.

The components of

are the coordinates of its terminal point when its initial point is at the origin. So,

⟨

⟩

The vector

has direction angle

so it lies on the positive

-axis

when its initial point is the origin. Since

the distance from the initial point of

to its terminal point is 7.

So,

⟨

⟩

Find

by adding the components of

and

⟨

⟩

⟨

⟩

⟨

⟩

Find the magnitude,

Use the formula for the magnitude of

8.062257…

≈

8.062

Find the direction angle,

To find the direction angle of

first determine which quadrant the point

(

)

lies in. Since both coordinates are positive, the point is in Quadrant I. So, the direction angle of

is:

tan

-1

≈

60.255°

This means the vector

makes a counterclockwise angle of approximately 60.255° with the positive

-axis.

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Not feeling ready yet? These can help:

Y.3Find the direction angle of a vector

Y.1Find the magnitude of a vector

Y.7Add vectors

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