# Worksheet: Dot Product

In this worksheet, we will practice using the dot product to find the magnitude of a vector.

**Q2: **

Square has side 10 cm. What is ?

**Q3: **

If and , find to the nearest hundredth.

**Q4: **

In rectangle , we have and . Determine to the nearest hundredth.

**Q5: **

.

- A
- B0
- C1
- D
- E

**Q6: **

In trapezium , with parallel sides and , suppose and are right angles, and that , while . Determine .

**Q7: **

In trapezium , with parallel sides and , suppose and are right angles and that , while . Determine .

**Q8: **

In trapezoid , with parallel sides and , suppose and are right angles, and that , while . Determine .

- A
2 916
- B
1 024.58
- C364.5
- D
1 458

**Q9: **

If find .

**Q10: **

If the two vectors and are perpendicular, determine the value of .

**Q11: **

If and , calculate the scalar product of and .

**Q12: **

and Find .

**Q13: **

Given that the norm of is 4 newtons in the direction of north of west, and the norm of is 21 meters in the direction of west, determine .

- A N⋅m
- B N⋅m
- C N⋅m
- D N⋅m

**Q14: **

If , , and , find the measure of the angle between the two vectors.

- A
- B
- C
- D

**Q15: **

is a trapezium, where , , , and , evaluate .

**Q16: **

Given that is an isosceles triangle, where and , determine correct to the nearest hundredth.

**Q17: **

If is an equilateral triangle of side 4.75, find approximated to the nearest hundredth.

**Q18: **

If is an equilateral triangle of side length 29.9 cm, find .

- A 1 788.02
- B 1 548.47
- C447.01
- D894.01

**Q19: **

Equilateral triangle has side 6.6. Find .

**Q20: **

Equilateral triangle has side 46.6. Find to the nearest hundredth.

**Q21: **

For the unit vectors , , , what is ?

**Q22: **

For the unit vectors , , , what is ?

**Q23: **

If is a parallelogram in which , , and , evaluate .

**Q24: **

Given that is an isosceles triangle, where and , determine .

**Q25: **

Given that is an equilateral triangle whose side length is 57 cm, and is the point of concurrency of its medians, evaluate .

- A
- B
- C270.75
- D
- E135.375