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In this lesson, we will learn how to determine the magnitude of two-dimensional vectors.

Q1:

Given that , find the value of .

Q2:

What is the magnitude of the vector ο π΄ π΅ , where π΄ = ( 5 , β 9 ) and π΅ = ( 9 , 1 ) ?

Q3:

The vector β π£ is shown on the grid of unit squares below. Find the value of β β β π£ β β .

Q4:

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

Q5:

What is the difference between scalar quantities and vector quantities?

Q6:

Displacement is a vector quantity which combines distance and direction. For example, the displacement of Washington, DC, from New York City is 200 miles southwest.

What is the magnitude of the displacement?

What is the direction of this displacement?

Q7:

Q8:

Q9:

Consider the vectors u = β¨ 2 , 3 β© and v = β¨ 4 , 6 β© .

What is the magnitude of u ? Give your answer correct to two decimal places if needed.

What is the magnitude of v ? Give your answer correct to two decimal places if needed.

What is the magnitude of u v + ? Give your answer correct to two decimal places if needed.

Q10:

What is the magnitude of the vector ?

Q11:

Q12:

The vector is shown on the grid of unit squares below. Find the value of .

Q13:

Which of the following is a direction vector for a line parallel to the π¦ -axis?

Q14:

Suppose the points π΄ and π΅ have coordinates ( π₯ , π¦ ) 1 1 and ( π₯ , π¦ ) 2 2 respectively. Find the magnitude of the vector ο π΄ π΅ in terms of π₯ 1 , π¦ 1 , π₯ 2 , and π¦ 2 .

Q15:

Q16:

Water boils at 2 1 2 β F . Is this temperature a scalar or vector quantity?

The freezing point of water is 1 8 0 β F lower than the boiling point of water. Is the freezing point of water a scalar or vector quantity?

Q17:

An astronomer observes a comet through her telescope and notes down its location. Which additional piece of information would allow her to predict the position of the comet in an hourβs time?

Q18:

Given that β π΄ = ( 2 , 1 4 ) , find β β β π΄ β β .

Q19:

Q20:

Q21:

Given that β π΄ = β 5 β π β 3 β π , where β π and β π are two perpendicular unit vectors, find β β β π΄ β β .

Q22:

Q23:

Q24:

Adel is 25 years old. Is his age a scalar or vector quantity?

Adelβs father is 31 years older than him. Is his fatherβs age a scalar or vector quantity?

Q25:

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

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