Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find the component of a vector in the direction of another vector.

Q1:

Consider the points π΄ ( 5 , β 1 , β 8 ) and π΅ ( β 3 , β 9 , β 6 ) . Find the component of the vector V i j k = β 5 β 2 + 2 in the direction ο« π΄ π΅ rounded to the nearest hundredth.

Q2:

Consider the points π΄ ( 7 , β 6 , 0 ) and π΅ ( β 5 , β 7 , β 4 ) . Find the component of the vector V i j k = β 8 β 9 β 3 in the direction ο« π΄ π΅ rounded to the nearest hundredth.

Q3:

Consider the points π΄ ( β 6 , 7 , 3 ) and π΅ ( β 7 , β 5 , β 2 ) . Find the component of the vector V i j = 5 β 9 in the direction ο« π΄ π΅ rounded to the nearest hundredth.

Q4:

Given that is a square having a side length of 53 cm, calculate the algebraic projection of in the direction of .

Q5:

π΄ π΅ πΆ π· is a trapezium, where ο« π΄ π· β₯ οͺ π΅ πΆ , π β π΄ = π β π΅ = 9 0 β , π β πΆ = 6 0 β , π΄ π· = 6 0 c m , and π΅ πΆ = 1 0 1 c m . Determine the algebraic projection of ο πΆ π· on the direction of ο πΆ π΅ .

Q6:

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are perpendicular.

Q7:

is a right-angled triangle in which , and . Determine the algebraic projection of in the direction of .

Q8:

Q9:

Given that the measure of the smaller angle between β π΄ and β π΅ is 1 5 0 β , and β β β π΅ β β = 5 4 , determine the component of vector β π΅ along β π΄ .

Q10:

If β β β π΄ β β = 5 , | | β π΅ | | = 1 5 , and the measure of the angle between them is 3 0 β , find the algebraic projection of β π΅ in the direction of β π΄ .

Q11:

Determine, to the nearest hundredth, the component of vector β π along ο π΄ π΅ , given that β π = ( β 7 , 2 , 1 0 ) and the coordinates of π΄ and π΅ are ( 1 , β 4 , β 8 ) and ( 3 , 2 , 0 ) , respectively.

Q12:

Determine, to the nearest hundredth, the component of vector β π along ο π΄ π΅ , given that β π = ( 5 , 7 , β 9 ) and the coordinates of π΄ and π΅ are ( β 1 , β 3 , β 5 ) and ( β 3 , β 1 0 , β 9 ) , respectively.

Q13:

Find the component of vector β π΄ in the direction of β π΅ , where π is the included angle between them.

Q14:

Determine the magnitude of the component of F i j = 2 3 + 1 7 in the direction of ο« π΄ π΅ , given that the coordinates of the points π΄ and π΅ are ( 2 , 3 ) and ( 6 , 6 ) respectively.

Q15:

Given that β π΄ = ( β 6 , 3 , β 2 ) and β π΅ = ( 4 , 1 , 6 ) , determine the component of β π΄ along β π΅ .

Donβt have an account? Sign Up