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In this lesson, we will learn how to use the dot product to find the magnitude of a vector.

Q1:

If β π΄ and β π΅ are unit vectors, which interval does β π΄ β β π΅ lie in?

Q2:

Square π΄ π΅ πΆ π· has side 10 cm. What is ο π΄ π΅ β ο π΅ πΆ ?

Q3:

If οΊ β π΄ + β π΅ ο β οΊ β π΄ β β π΅ ο = 5 7 and β β β π΄ β β = 3 β β β π΅ β β , find β β β π΄ β β to the nearest hundredth.

Q4:

In rectangle π΄ π΅ πΆ π· , we have π΄ π΅ = 1 5 and π΅ πΆ = 1 1 . Determine οΊ ο π΅ πΆ ο β οΊ 5 ο π· π΅ ο to the nearest hundredth.

Q5:

β π΄ β β π΄ = .

Q6:

In trapezium π΄ π΅ πΆ π· , with parallel sides π΄ π· and π΅ πΆ , suppose β π΄ and β π΅ are right angles, and that π΄ π΅ = 1 2 π΅ πΆ = 2 9 . 8 , while πΆ π· = 3 9 . Determine ο π· π΅ β ο π΅ πΆ .

Q7:

In trapezium π΄ π΅ πΆ π· , with parallel sides π΄ π· and π΅ πΆ , suppose β π΄ and β π΅ are right angles and that π΄ π΅ = 1 2 π΅ πΆ = 3 7 , while πΆ π· = 3 9 . Determine ο π· πΆ β ο π΄ π΅ .

Q8:

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

Q9:

If find .

Q10:

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

Q11:

If β π΄ = 2 β π and β π΅ = β π β 9 β π , calculate the scalar product of β π΄ and β π΅ .

Q12:

and Find β π΄ β β π΅ .

Q13:

Given that the norm of A is 4 newtons in the direction of 4 5 β north of west, and the norm of B is 21 meters in the direction of west, determine A B β .

Q14:

If β β β π΄ β β = 1 7 , β β β π΅ β β = 1 2 , and β π΄ β β π΅ = 1 0 2 , find the measure of the angle between the two vectors.

Q15:

π΄ π΅ πΆ π· is a trapezium, where π΄ π· β₯ π΅ πΆ , π β π΄ = π β π΅ = 9 0 β , π΄ π· = 1 2 π΅ πΆ = 2 0 c m , and πΆ π· = 2 2 c m , evaluate ο π΅ π· β ο π΅ π΄ .

Q16:

Given that π΄ π΅ πΆ is an isosceles triangle, where π΄ π΅ = π΄ πΆ = 1 9 c m and π β π΄ = 5 1 β , determine ο π΅ π΄ β ο π΅ πΆ correct to the nearest hundredth.

Q17:

If π΄ π΅ πΆ is an equilateral triangle of side 4.75, find ο π΄ π΅ β ο π΄ πΆ approximated to the nearest hundredth.

Q18:

If π΄ π΅ πΆ is an equilateral triangle of side length 29.9 cm, find ο π΄ π΅ β οΊ ο π΄ πΆ + ο πΆ π΅ ο .

Q19:

Equilateral triangle π΄ π΅ πΆ has side 6.6. Find οΊ 6 ο π΄ πΆ ο β οΊ 5 ο πΆ π΅ ο .

Q20:

Equilateral triangle π΄ π΅ πΆ has side 46.6. Find ο π΄ π΅ β ο π΅ πΆ to the nearest hundredth.

Q21:

For the unit vectors β π , β π , β π , what is β π β β π ?

Q22:

For the unit vectors β π , β π , β π , what is β π β β π ?

Q23:

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

Q24:

Given that π΄ π΅ πΆ is an isosceles triangle, where π΄ π΅ = π΄ πΆ = 6 c m and π β π΄ = 1 2 0 β , determine ο πΆ π΄ β ο π΅ πΆ .

Q25:

Given that π΄ π΅ πΆ is an equilateral triangle whose side length is 57 cm, and π is the point of concurrency of its medians, evaluate ο π π· β ο π πΉ .

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