# Worksheet: Cross Product in 2D

In this worksheet, we will practice finding the cross product of two vectors in the coordinate plane.

Q1:

All the sides of rhombus are of length 5. Suppose that and that . Use vector multiplication to find the lengths of the two diagonals.

• A,
• B,
• C,
• D,

Q2:

A rectangle has vertices , , , and . Use vectors to determine its area.

Q3:

Given that and , determine the area of the parallelogram whose adjacent sides are represented by and .

Q4:

If and , find .

Q5:

is a square of side 4, and is a unit vector perpendicular to the square’s plane. Find . Q6:

In the rectangle shown in the figure, calculate if form a right-hand system of unit vectors. • A
• B
• C
• D

Q7:

If , , , and , find .

• A
• B
• C
• D

Q8:

Given that , , and , determine .

• A
• B
• C
• D

Q9:

If , , , and , find .

• A
• B
• C
• D

Q10:

If , , and , find the value of .

Q11:

Given that is a square with side length 27 cm, and is the unit vector perpendicular to its plane, determine .

• A
• B
• C
• D

Q12:

Given that is a square with side 49, and is the unit vector perpendicular to its plane, determine .

• A
• B
• C
• D

Q13:

If is a square with a side length of 81 cm, and is a unit vector perpendicular to its plane, find .

• A
• B
• C
• D

Q14:

is a rectangle where is a unit vector perpendicular to its plane. Find . • A
• B
• C
• D

Q15:

is a rectangle where is a unit vector perpendicular to its plane. Find . • A
• B
• C
• D

Q16:

Given that , and , and , find the value of .

• A
• B
• C
• D
• E

Q17:

Find the value of .

• A
• B2
• C1
• D
• E0

Q18:

Find the area of a triangle , where , , and .

Q19:

is a rhombus, in which the coordinates of the points and are and , respectively. Use vectors to determine its perimeter.

• A length units
• B length units
• C length units
• D666 length units

Q20:

Rhombus has vertices , , , and . Use vectors to determine its area.