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In this lesson, we will learn how to express vectors in terms of fundamental unit vectors instead of component form and how to add and subtract vectors in that form.

Q1:

Find the unit vector in the direction of the π₯ -axis.

Q2:

Given that β π΄ and β π΅ are two unit vectors, and β β β π΄ + β π΅ β β = 1 , evaluate οΊ 6 β π΄ + 4 β π΅ ο β οΊ β 2 β π΄ + β π΅ ο .

Q3:

Find the unit vector in the direction of the π¦ -axis.

Q4:

Suppose that β π΄ = ( 5 , 9 , 9 ) , β π΅ = ( β 4 , β 2 , β 9 ) , and β π΄ + β π΅ + β πΆ = β π . What is β πΆ ?

Q5:

Suppose that β π΄ = ( 4 , 7 , β 7 ) , β π΅ = ( β 5 , 1 , β 2 ) , and β π΄ + β π΅ + β πΆ = β π . What is β πΆ ?

Q6:

Given that β π΄ = 3 β π + β π + π β π and that β π΅ is a unit vector equal to 1 5 β π΄ , determine the possible values of π .

Q7:

Is β π΄ = οΌ 2 3 , 2 3 , 1 4 ο a unit vector?

Q8:

Find the unit vector in the direction of the π§ -axis.

Q9:

If and are unit vectors and the measure of the angle between them, find .

Q10:

Suppose a unit vector β π΄ is such that 1 1 β π΄ = ( β 1 , β 2 , π ) . Determine the possible values of π .

Q11:

If β π΄ = 4 β π + 4 β π β 5 β π and β π΅ = 3 β π β β π , determine β β β π΄ β β π΅ β β .

Q12:

If β π΄ = 3 β π β β π β 4 β π and β π΅ = β 3 β π + 5 β π β 5 β π , determine β β β π΄ β β π΅ β β .

Q13:

If β π΄ = 5 β π β 2 β π β β π and β π΅ = β β π + 2 β π , determine β β β π΄ + β π΅ β β and β β β π΄ β β + β β β π΅ β β .

Q14:

If β π΄ = β 2 β π β 3 β π + 4 β π and β π΅ = β 4 β π β 4 β π β 3 β π , determine β β β π΄ + β π΅ β β and β β β π΄ β β + β β β π΅ β β .

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