MATH_19732

Question 1

If the dot product of 2 vectors is zero, it means that…?

Answer 1

The vectors are perpendicular to each other

Question 2

If the cross product of 2 vectors is zero, it means that…?

Answer 2

The vectors are collinear

There is no angle between them

Question 3

Give the equation for area of a triangle in vector form

Answer 3

0.5 x |AB X AC|

Where |AB X AC| is the modulus of the cross product of the two vectors

Question 4

How does the formula for the dot product differ from the cross product?

Answer 4

In the dot product, the cosine of the angle is taken, in the vector product, the sine of the angle is taken.

Question 5

True or False:

The cross product of two vectors is orthogonal to both of them

Answer 5

True

Question 6

How is the direction of the vector product determined?

vector product == cross product

Answer 6

By the right hand rule

The thumb points in the direction of the first vector
The index points in the direction of the second vector
The middle finger points in the direction of the vector product

Question 7

What does the modulus of a vector determine when it is drawn?

Answer 7

Its length

Question 8

On what condition can the product AB of two matrices A and B respectively be performed?

Answer 8

If the number of columns in A are equal to the number of rows in B

Question 9

What is the value of i ?

Answer 9

√-1

Question 10

What is the general form for the rotational matrix in two dimensions?

Answer 10

|cos (Φ) -sin(Φ)|
|sin(Φ) cos(Φ)|

Question 11

How can you check if a given square matrix has an inverse (without too much solving)

Answer 11

Get the determinant

If the determinant is ≠ 0, the matrix is invertible

Question 12

What are the three ways you can describe a complex number?

Answer 12

1. Using the plane coordinates (a and b)
2. Using the argument and modulus (θ and r)

Where
a is the coordinate of the **real component **
b is the coordinate of the imaginary component of the complex number
r is the distance between the complex number coordinate and the origin
and θ is the angle between r and the real axis

Question 13

Transpose the given matrix

|2 3 4|
|1 5 2|

Answer 13

|2 1|
|3 5|
|4 2|

Question 14

What is the dimension of this matrix ?

|2 4 6 8|
|1 5 2 9|

(m x n)?

Answer 14

2 x 4

You state the number of roows first

Question 16

What are the two ways you can describe a plane?

Answer 16

1. Using 3 points on it
2. Using 2 points on the plane and a line