Q: For the vector $$\vec{A} = (a, b)$$, what is the formula for its magnitude and angle relative to the $$+x-$$axis?

$$r = \sqrt{a^2$ + b^2$},\ \theta = \tan$$^{-1}$$\left(\frac{b}{a}\right)$$

Question 1

Which of the following best describes what a unit for a physical quantity indicates?

Accepted Answer

what the number means

Question 2

What makes a number physically meaningful in physics?

Accepted Answer

Unit

Question 3

The SI unit system is also known as:

Accepted Answer

the MKS unit system

Question 4

In the MKS unit system, what does the 'M' stand for?

Accepted Answer

meter (m)

Question 5

A vector has magnitude and which other property?

Accepted Answer

direction (angle)

Question 6

Two vectors are considered the same if they have the same magnitude and direction, regardless of their:

Accepted Answer

position (location)

Question 7

Given points $$A(2,1)$$ and $$B(5,3)$$, what are the $$x$$ and $$y$$ components of $$\overrightarrow{AB}$$?

Accepted Answer

$$3,2$$

Question 8

Find the magnitude of the vector $$\vec{A} = (3,4).$$

Accepted Answer

$$5$$

Question 9

For the vector $$\vec{A} = (a, b)$$, what is the formula for its magnitude and angle relative to the $$+x-$$axis?

Accepted Answer

$$r = \sqrt{a^2$ + b^2$},\ 	heta = 	an$$^{-1}$$\left(\frac{b}{a}ight)$$

Question 10

Which of the following is the correct formula for the $$x$$ and $$y$$ components of a vector with magnitude $$r$$ and angle $$	heta$$ relative to the $$+x-$$axis?

Accepted Answer

$$(r\cos	heta, r\sin	heta)$$

Question 11

The scalar (dot) product $$\vec{A} \cdot \vec{B} is $$most closely related to which type of physical motion?

Accepted Answer

pulling forward motion

Question 12

Find $$\vec{A} \cdot \vec{B}$$ where $$\vec{A} = (2,4)$$ and $$\vec{B} = (3,1).$$

Accepted Answer

$$10$$

Question 13

Find $$\vec{A} 	imes \vec{B}$$ where $$\vec{A} = (2,4,3)$$ and $$\vec{B} = (5,1,2). $$Use the determinant method.

Accepted Answer

$$(-4, 11, -18)$$

Question 14

What is the result of $$\hat{i} \cdot \hat{j}$$?

Accepted Answer

$$0$$

Question 15

For the origin $$O$$ and point $$A(a, b) on $$the $$xy-$$plane, express vector $$\overrightarrow{OA} in $$terms of $$\hat{i}$$ and $$\hat{j}.$$

Accepted Answer

$$a\hat{i} + b\hat{j}$$

Question 16

A vector can be described either by magnitude and angle (direction) or by which other pair?

Accepted Answer

$$x-$$component, $$y-$$component

Question 17

Find $$\vec{A} \cdot \vec{B}$$ where $$\vec{A} = (3,1,2)$$ and $$\vec{B} = (5,1,-2).$$

Accepted Answer

$$12$$

Question 18

The magnitude of a unit vector is:

Accepted Answer

$$1$$

Question 19

For the vector subtraction $$\vec{A} - \vec{B} = \overrightarrow{BA}$$, what does $$\overrightarrow{BA}$$ represent?

Accepted Answer

How to get to $$A$$ from $$B$$

CH. 1 - Physics with Calculus: Vectors, Units, and Vector Operations Study Guide

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