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In this lesson, we will learn how to recognize, construct, and express directed line segments.

Q1:

In the given parallelogram π΄ π΅ πΆ π· , π΄ πΆ β© π΅ π· = { π } , πΈ is the midpoint of π΄ π΅ , and πΉ is the midpoint of π΅ πΆ . Complete the following: 1 2 ο π΄ πΆ is equivalent to .

Q2:

Given that β π΄ = β 9 β π β 7 β π , where β π and β π are two perpendicular unit vectors, find β 1 2 β π΄ .

Q3:

Given that the vectors and are perpendicular, find the value of .

Q4:

Given that π΄ π΅ πΆ π· is a square of side length 9 cm, determine the scalar product of οΊ 2 ο π· π΅ ο and οΌ 3 5 ο π΅ π΄ ο .

Q5:

Given that is a rectangle in which cm and cm, define the algebraic projection of in the direction of .

Q6:

If π΄ π΅ πΆ π· is a rectangle in which π΄ π΅ = 1 0 c m and π΅ πΆ = 6 c m , evaluate οΌ β 1 2 ο π΅ π· ο β οΌ 1 2 ο π΅ πΆ ο .

Q7:

If π΄ π΅ πΆ π· is a rhombus in which π΄ πΆ = 1 5 c m and π΅ π· = 2 0 c m , evaluate οΌ 7 1 0 ο π· πΆ ο β οΌ 3 5 ο π΄ πΆ ο .

Q8:

Given that ο π = οΌ 5 2 , 2 ο , express the vector ο π in terms of the unit vectors β π and β π , and find its norm β β ο π β β .

Q9:

Given that β π΄ = ( π , β 4 ) , β π΅ = ( β 4 , π ) , and β π΄ = 2 β π΅ , determine the values of π and π .

Q10:

Find the magnitude of the vector β π£ shown on the grid of unit squares below.

Q11:

Find the components of the vector β π£ shown on the grid of unit squares below.

Q12:

Find the magnitude of the vector shown on the grid of unit squares below.

Q13:

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