Vector Operations and Properties

Vector Operations and Properties

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers solving a quiz question involving vectors. It starts with defining vectors and calculating the direction angle using the arc tangent. The tutorial then explains how to find unit vectors orthogonal to a given vector B. It proceeds to calculate the area using vector norms and angles. Finally, it demonstrates solving for values of K that result in obtuse angles between vectors, using dot products and graphing techniques.

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19 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the components of vector A?

3, -9

2, -3

1, 0

-5, 4

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving 2A - 3B?

Find the magnitude of A

Determine the angle between vectors

Define vectors A and B

Calculate the dot product

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the direction angle determined?

Using arc sine

Using arc cosine

Using arc tangent

Using arc cotangent

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the process to find a unit vector orthogonal to B?

Subtract components and normalize

Swap components and change one sign

Add components and divide by magnitude

Multiply components by a scalar

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of rationalizing a unit vector?

To make it orthogonal

To increase its magnitude

To change its direction

To simplify calculations

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of the dot product of B and its orthogonal unit vector?

Undefined

1

-1

0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find a second orthogonal unit vector?

Add a scalar to the first vector

Multiply the first vector by -1

Divide the first vector by 2

Subtract a scalar from the first vector

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