Unit Vectors

Unit Vectors

Precalculus C6​

By natalie richardson

A unit vector has a magnitude of 1.

In many applications of vectors, it is useful to find a unit vector that has the same direction as a given nonzero vector v.

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Unit Vectors

To find a unit vector, divide vector v by its length (magnitude).

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Unit Vectors

• Note that u is a scalar multiple of v

• Vector u has a magnitude of 1

• Vector u has the same direction as v

• Vector u is called a unit vector in the direction of v​

Unit Vectors

Find a unit vector in the direction of v = <-2,5>. Verify that the result has a magnitude of 1.

Multiple Choice

Find the unit vector in the direction of v = <-3,3>.

• <-3,3>

• $$<\frac{-1}{3\sqrt[]{2}},\frac{1}{3\sqrt[]{2}}>$$  

• <-3/18, 3/18>

• $$<\frac{-1}{\sqrt[]{2}},\frac{1}{\sqrt[]{2}}>$$  

Multiple Choice

Find the unit vector in the direction of v = <5,12>.

• <5,12>

• $$<\frac{5}{13},\frac{12}{13}>$$  

• $$<\frac{5}{\sqrt[]{13}},\frac{12}{\sqrt[]{13}}>$$  

• $$<\frac{5}{\sqrt[]{2}},\frac{12}{\sqrt[]{2}}>$$  

Multiple Choice

Find the unit vector n the direction of v = <-5,7>.

• <-5,7>

• $$<-\frac{5}{\sqrt[]{74}},\frac{7}{\sqrt[]{74}}>$$  

• <-5/24, 7/24>

• $$<\frac{-5}{\sqrt[]{24}},\frac{7}{\sqrt[]{24}}>$$  

Multiple Choice

Find the unit vector n the direction of v = <3,-8>.

• <3,-8>

• $$<\frac{3}{\sqrt[]{73}},\frac{-8}{\sqrt[]{73}}>$$  

• $$<\frac{3}{73},-\frac{8}{73}>$$  

• $$<\frac{3}{\sqrt[]{75}},\frac{-8}{\sqrt[]{75}}>$$  

Multiple Select

What are the standard unit vectors. Select all that apply.

• <0, 1>

• <1, 1>

• <0,0>

• <1,0>

Multiple Choice

What is the horizontal component of $$v=<v_1,v_2>$$  

• $$v_1$$  

• $$v_2$$  

• none of these

Multiple Choice

What is the vertical component of $$v=<v_1,v_2>$$  

• $$v_1$$  

• $$v_2$$  

• none of these

Multiple Choice

Write $$v=<v_1,\ v_2>$$   as a linear combination of i and j.

• $$v_1\ +\ v_2$$  

• $$v_1i\ +\ v_2i$$  

• $$v_1i\ +\ v_2j$$  

• $$v_1j\ +\ v_2i$$  

Multiple Choice

Write vector v = <-5, 7> as a linear combination of standard unit vectors.

• <-5,7>

• -5 + 7

• -5i + 7j

Multiple Choice

Write vector v = <-15, -11> as a linear combination of standard unit vectors.

• -15i - 11j

• -15i + 11j

• <-15i, -11j>

Let v be the vector with initial point (2,-5) and terminal point (-1,3). Write v as a linear combination of the standard unit vectors.

Multiple Choice

Let v be the vector with initial point (2,-5) and termiinal point (-1,3). Write v as a linear combination of the standard unit vectors..

• 3i + 8j

• -3i - 8j

• -3i + 8j

Multiple Choice

Let v be the vector with initial point (3,-5) and termiinal point (7,2). Write v as a linear combination of the standard unit vectors..

• 4i + 7j

• -5i - 7j

• 10i + -3j

Multiple Choice

If u = -3i + 8j, find 2u.

• -3i + 16j

• -6i + 16j

• 6i - 16j

Multiple Choice

If v = 2i - j, find -3v.

• 6i + 3j

• -6i - 3j

• -6i + 3j

Multiple Choice

Let u = -3i + 8j and v=2i - j. Find 2u - 3v.

• -12i + 19j

• -10i - 7j

• -i + -7j

Multiple Choice

Let u = -3i + 8j and v=2i - j. Find -3u + 2v.

• -i + 7j

• -5i - 22j

• 13i - 26j