IXL - Find the component form of a vector from its magnitude and direction angle (Precalculus practice)

The magnitude of a vector

is 6 and its direction angle

is 90°. Write the component form for

Write each component in exact simplified form.

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question

The magnitude of a vector

is 11 and its direction angle

is 90°. Write the component form for

Write each component in exact simplified form.

key idea

A vector is a quantity that has both a length and a direction.

The length of a vector

is called the magnitude, which is written

The direction of

can be specified by the counterclockwise angle

from the positive

-axis

called the direction

angle.

The component form of a vector

with direction angle

⟨

cos

(

)

sin

(

)

⟩

The first component,

cos

(

)

is the horizontal change, and the second component,

sin

(

)

is the vertical change.

solution

You are given

and

90°

Find the component form.

⟨

cos

(

𝜃

)

sin

(

𝜃

)

⟩

⟨

cos

(

)

sin

(

)

⟩

⟨

(

)

(

)

⟩

⟨

⟩

Since the first component of

is 0,

is vertical and lies on the positive

-axis.

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Not feeling ready yet? These can help:

R.12Trigonometric ratios: find a side length

Y.3Find the direction angle of a vector

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