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In this lesson, we will learn how to use the vector product of two vectors in a geometrical context.

Q1:

Find the area of a triangle π΄ π΅ πΆ , where π΄ ( β 8 , β 9 ) , π΅ ( β 7 , β 8 ) , and πΆ ( 9 , β 2 ) .

Q2:

Find the area of a triangle π΄ π΅ πΆ , where π΄ ( 0 , 5 ) , π΅ ( 7 , β 9 ) , and πΆ ( β 1 , 0 ) .

Q3:

Find the area of a triangle π΄ π΅ πΆ , where π΄ ( 9 , β 3 ) , π΅ ( β 3 , β 2 ) , and πΆ ( β 9 , 2 ) .

Q4:

Find the area of a triangle π΄ π΅ πΆ , where π΄ ( 1 , 4 ) , π΅ ( β 7 , 6 ) , and πΆ ( β 9 , β 5 ) .

Q5:

Assuming that ( β π , β π , β π ) form a right-hand system, β π΄ = 1 6 β π + 4 β π , β π΅ = 1 9 β π + 8 β π , and β π΄ and β π΅ form two adjacent sides of a triangle, find the vector product of β π΄ into β π΅ and the area of the triangle drawn.

Q6:

π΄ π΅ πΆ π· is a rhombus, in which the coordinates of the points π΄ and π΅ are ( 5 , β 9 ) and ( β 1 0 , 1 2 ) , respectively. Use vectors to determine its perimeter.

Q7:

If π΄ π΅ πΆ is a triangle of area 248.5 cm^{2}, find the value of β β ο π΅ π΄ Γ ο π΄ πΆ β β .

Q8:

Rhombus π΄ π΅ πΆ π· has vertices π΄ ( β 4 , 6 ) , π΅ ( 9 , 2 ) , πΆ ( β 2 , 1 0 ) , and π· ( β 1 5 , 1 4 ) . Use vectors to determine its area.

Q9:

Rhombus π΄ π΅ πΆ π· has vertices π΄ ( 7 , β 6 ) , π΅ ( 0 , β 2 ) , πΆ ( β 1 , 6 ) , and π· ( 6 , 2 ) . Use vectors to determine its area.

Q10:

Rhombus π΄ π΅ πΆ π· has vertices π΄ ( 5 , 6 ) , π΅ ( β 5 , 1 ) , πΆ ( β 3 , 1 2 ) , and π· ( 7 , 1 7 ) . Use vectors to determine its area.

Q11:

Rhombus π΄ π΅ πΆ π· has vertices π΄ ( 6 , 1 0 ) , π΅ ( 2 , β 7 ) , πΆ ( β 5 , 9 ) , and π· ( β 1 , 2 6 ) . Use vectors to determine its area.

Q12:

Given that π· = ( 0 , β 2 , β 8 ) , πΈ = ( 6 , 4 , 6 ) , and πΉ = ( β 4 , β 9 , β 2 ) , determine the area of the triangle π· πΈ πΉ approximated to the nearest hundredth.

Q13:

Given that π· = ( β 2 , 0 , β 2 ) , πΈ = ( β 3 , β 9 , 5 ) , and πΉ = ( β 5 , β 1 , β 6 ) , determine the area of the triangle π· πΈ πΉ approximated to the nearest hundredth.

Q14:

Triangle π΄ π΅ πΆ has vertices π΄ ( 5 , β 4 ) , π΅ ( β 1 , β 5 ) , and πΆ ( β 3 , 2 ) . Use vectors to determine its area.

Q15:

Suppose that β π΄ = ( 1 , 1 , 3 ) and β π΅ = ( 4 , 8 , β 8 ) fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

Q16:

Suppose that β π΄ = ( β 5 , 4 , 5 ) and β π΅ = ( β 1 , 8 , 2 ) fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

Q17:

Suppose that β π΄ = ( β 2 , β 8 , 8 ) and β π΅ = ( 3 , β 3 , β 3 ) fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

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