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In this lesson, we will learn how to find the cross product of two vectors in space.

Q1:

Let and . Calculate .

Q2:

Given that β π΄ = β 9 β π β β π + 3 β π and β π΅ = 3 β π β 2 β π β 7 β π , determine β π΄ Γ β π΅ .

Q3:

Given that β π΄ = ( β 5 , β 9 , β 1 ) and β π΅ = ( 2 , β 1 , β 7 ) , find β π΄ Γ β π΅ .

Q4:

Given that β π΄ = β 3 β π + 3 β π β 5 β π and β π΅ = β β π β 3 β π + 5 β π , determine οΊ 4 β π΄ ο Γ οΊ 2 β π΅ ο .

Q5:

If β π΄ = ( 4 , β 2 , β 9 ) and β π΅ = ( 4 , 3 , 4 ) , determine β π΄ Γ β π΅ .

Q6:

If the force β πΉ = π₯ β π + 2 β π is acting at the point π΄ ( 9 , β 4 ) , where its moment vector about the point π΅ ( 8 , β 2 ) is 8 β π , determine the value of π₯ .

Q7:

Given that the forces β πΉ = β β π + π β π 1 , β πΉ = β 2 β π β 8 β π 2 , and β πΉ = π β π β 1 2 β π 3 are three parallel forces, find the values of π and π .

Q8:

and are two vectors, where and . Calculate .

Q9:

β π and ο π are two vectors, where β π = β β π + 2 β π + β π and ο π = β 3 β π + 6 β π + 3 β π . Calculate β π Γ ο π .

Q10:

Q11:

If β π΄ = ( 3 , 4 , β 4 ) , β π΅ = ( 2 , 5 , β 4 ) , and β πΆ = ( β 4 , β 4 , 2 ) , find οΊ β π΄ β β π΅ ο Γ οΊ β πΆ β β π΄ ο .

Q12:

Find the unit vectors that are perpendicular to both β π΄ = ( 4 , 2 , 0 ) and β π΅ = ( 4 , 6 , β 4 ) .

Q13:

Q14:

Given that β π΄ = ( β 3 , 4 , 0 ) , and β π΅ = ( 1 , β 5 , 1 ) , determine the unit vector perpendicular to the plane of the two vectors β π΄ and β π΅ .

Q15:

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