maths 2

Question 1

Define vector.

Answer 1

A quantity with both magnitude and direction.

Question 2

What is the Pythagorean theorem?

Answer 2

A formula stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Question 3

True or false: Vectors can be added geometrically.

Answer 3

TRUE

Vectors can be added using the head-to-tail method.

Question 4

Fill in the blank: The magnitude of a vector is its _______.

Answer 4

length

Question 5

What is the formula for the magnitude of a vector?

Answer 5

Magnitude = √(x² + y²) for 2D vectors.

Question 6

Define unit vector.

Answer 6

A vector with a magnitude of 1.

Question 7

Fill in the blank: The dot product of two vectors is a _______.

Answer 7

scalar

Question 8

What does the cross product of two vectors yield?

Answer 8

A vector that is perpendicular to both original vectors.

Question 9

True or false: The Pythagorean theorem applies to all triangles.

Answer 9

FALSE

It only applies to right triangles.

Question 10

What is the resultant vector?

Answer 10

The vector sum of two or more vectors.

Question 11

Define orthogonal vectors.

Answer 11

Vectors that are perpendicular to each other.

Question 12

Fill in the blank: The angle between two vectors can be found using the _______.

Answer 12

dot product

Question 13

What is the distance formula derived from the Pythagorean theorem?

Answer 13

Distance = √((x2 - x1)² + (y2 - y1)²).

Question 14

True or false: Vectors can be represented graphically.

Answer 14

TRUE

Vectors are often represented as arrows in a coordinate system.

Question 15

What is the angle of elevation?

Answer 15

The angle between the horizontal line and the line of sight to an object above.

Question 16

Define component form of a vector.

Answer 16

A representation of a vector using its horizontal and vertical components.

Question 17

Fill in the blank: The slope of a line can be found using _______.

Answer 17

rise over run

Question 18

What is the formula for the area of a triangle using vectors?

Answer 18

Area = 1/2 |A × B|, where A and B are two vectors.

Question 19

True or false: The magnitude of a vector can be negative.

Answer 19

FALSE

Magnitude is always a non-negative value.

Question 20

What is the projection of vector A onto vector B?

Answer 20

The component of A in the direction of B.

Question 21

Define scalar multiplication of a vector.

Answer 21

Multiplying a vector by a scalar changes its magnitude but not its direction.

Question 22

Fill in the blank: The angle between two vectors can be calculated using the _______.

Answer 22

cosine of the dot product

Question 23

What is the formula for the distance between two points?

Answer 23

Distance = √((x2 - x1)² + (y2 - y1)²).

Question 24

True or false: Vectors can exist in three-dimensional space.

Answer 24

TRUE

3D vectors include a z-component in addition to x and y.

Question 25

What is the **law of cosines**?

Answer 25

A formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Question 26

Define **vector addition**.

Answer 26

The process of adding two or more vectors to find a resultant vector.

Question 27

Fill in the blank: The **length** of a vector is also called its _______.

Answer 27

magnitude

Question 28

What is the **angle of depression**?

Answer 28

The angle between the horizontal line and the line of sight to an object below.

Question 29

True or false: The components of a vector can be negative.

Answer 29

TRUE ## Footnote Negative components indicate direction in the opposite axis.

Question 30

What is the **formula** for the area of a parallelogram using vectors?

Answer 30

Area = |A × B|, where A and B are two adjacent sides.

Question 31

Define **vector subtraction**.

Answer 31

The process of finding the difference between two vectors.

Question 32

Fill in the blank: The **unit vector** in the direction of vector A is _______.

Answer 32

A divided by its magnitude.

Question 33

What is the **resultant** of vectors A and B?

Answer 33

A vector that represents the combined effect of A and B.

Question 34

True or false: The Pythagorean theorem can be extended to three dimensions.

Answer 34

TRUE ## Footnote In 3D, a² + b² + c² = d² applies.

Question 35

What is the **direction** of a vector?

Answer 35

The angle it makes with a reference axis.

Question 36

Define **linear combination** of vectors.

Answer 36

A vector formed by adding together scalar multiples of other vectors.