Determine if the following statement is true or false : The vectors v v and − v -v point in the same direction.

this problem, we are asked to determine if the following statement is true or false, and we have that vectors 'v' and negative 'v' point in the same direction. How could we solve this? Well, I'm going to start by drawing a random vector 'v' over here. So let's say that this is our vector and we'll call this 'v'. Now what I need to do next is draw vector negative 'v', and recall that a negative vector actually has the same magnitude as the original vector, but what about the direction? Well, it turns out that whenever you have a negative sign in front of the original vector, it's going to change the direction to the opposite side. So vectors v and negative v will point in opposite directions. And because these point opposite directions, we would say that this statement is false. Vectors 'v' and 'negative v' do not point in the same directions. I hope you found this video helpful.

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0. Review of College Algebra4h 43m

Rationalizing Denominators
15m

Pythagorean Theorem & Basics of Triangles
17m

Basics of Graphing
30m

Functions
41m

Transformations
45m

Asymptotes
4m

Solving Linear Equations
31m

Solving Quadratic Equations
55m

Complex Numbers
41m

1. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

2. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

3. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

4. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

6. Trigonometric Identities and More Equations2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

7. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

9. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

10. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

11. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

8. Vectors

Geometric Vectors

Trigonometry

8. Vectors

Geometric Vectors

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Multiple Choice

Determine if the following statement is true or false: The vectors $v$ and $- v$ point in the same direction.

True

False

Cannot be determined

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Verified step by step guidance

Understand the concept of vector direction: A vector has both magnitude and direction. The direction of a vector is indicated by the direction of the arrow.

Consider the vector v: The vector v has a specific direction, which is determined by the orientation of the arrow.

Consider the vector -v: The vector -v is the negative of vector v, meaning it has the same magnitude but points in the opposite direction.

Compare the directions: Since -v is the negative of v, it points in the opposite direction to v.

Conclude the statement: Based on the comparison, the vectors v and -v do not point in the same direction, thus the statement is false.

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Struggling with Trigonometry?

Determine if the following statement is true or false: The vectors vv and −v-v point in the same direction.

Watch next

Geometric Vectors practice set

Determine if the following statement is true or false: The vectors $v$ and $- v$ point in the same direction.