1.3.2 Vector Components and Unit Vectors

Question 1

Vector Components and Unit Vectors

Answer 1

• A vector is a quantity that includes both magnitude and direction.
• You can think of a vector in two ways:- in terms of its magnitude and its direction (angle)- in terms of how far it goes horizontally and how far it goes vertically (its x- and y- components)
• A unit vector can have any direction, but its length must equal one.
• To multiply a vector in component form by a scalar, multiply the components by the scalar. To add (or subtract) two vectors in component form, add (or subtract) the components.

Question 2

note 1

Answer 2

• Instead of thinking of a vector in terms of its magnitude and direction, it is often useful to think of it in terms of its x- and y- components.
• Here, the x- and y-components of the vector are labeled and . They are a measure of how far extends in the horizontal and vertical directions, respectively.
• Using the formulas shown, you can determine the x- and y-components of a vector from its magnitude (A) and direction(u), and vice versa.
• To write a vector in terms of its components, our convention is to use the unit vectors and . Unit vectors will also come in handy in other situations. They are always denoted with a hat rather than an arrow on top of the vector symbol.
• When a vector is written in component form, it is easy to perform scalar multiplication. Simply distribute the scalar to all the terms like you normally would.
• It is just as easy to add or subtract vectors in component form. Just write out the sum or difference and combine like terms.

Question 3

note 2

Answer 3

• in this example, you are given the magnitudes and directions of two vectors and asked to find their sum.
• To solve the problem, find the x- and y-components of and. Be careful when applying the conversion formulas presented earlier to – the angle given in the diagram (30°)is not the angle from the horizontal, as the formula expects.
• Once you have and in terms of their components, finding the sum is just a matter of addition.

Question 4

Which of the following does not correctly describe each given vector in terms of the unit vectors? (Note that each grid line is half of a unit.)

Answer 4

V B = -4 j

Question 5

Which of the following explains how to describe a vector?

Answer 5

Vectors can be described using magnitude and direction, using an x- and y-coordinate system, or using unit vectors.

Question 6

What is the magnitude of vector A?

Answer 6

6.00 cm

Question 7

Which of the following statements related to vectors is not correct?

Answer 7

A “one way” road sign is an example of a vector.

Question 8

what is the correct value for theta and a in the given right triangle?

Answer 8

theta = 36.9 degrees and a = 53.1 degrees