# Worksheet: Cross Product in 3D

In this worksheet, we will practice finding the cross product of two vectors in space and how to use it to find the area of geometric shapes.

Q1:

Let and . Calculate .

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Q2:

Given that and , determine .

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Q3:

Given that and , find .

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Q4:

Given that and , determine .

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Q5:

If and , determine .

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Q6:

and are two vectors, where and . Calculate .

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Q7:

and are two vectors, where and . Calculate .

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Q8:

and are two vectors, where and . Calculate .

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Q9:

If , , and , find .

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Q10:

Find the unit vectors that are perpendicular to both and .

• A or
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Q11:

and are two vectors, where and . Calculate .

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Q12:

Given that , and , determine the unit vector perpendicular to the plane of the two vectors and .

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Q13:

Let and . Calculate .

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Q14:

Assuming that form a right-hand system, , , and and form two adjacent sides of a triangle, find the vector product of and and the area of the triangle drawn.

• A, area square units
• B, area square units
• C, area square units
• D, area square units
• E, area square units

Q15:

Given that the area of is 340, what is ?

Q16:

If is a triangle of area 248.5 cm2, find the value of .

Q17:

Given that , , and , determine the area of the triangle approximated to the nearest hundredth.

Q18:

Triangle has vertices , , and . Use vectors to determine its area.

Q19:

Suppose that and fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

Q20:

If and , find .

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Q21:

If and , find .

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Q22:

If , , and , find .

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Q23:

Given that , , , and , find .

Q24:

Given that the vectors and are parallel, determine the value of .

Q25:

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

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