7.8 Chapter Test
Chapter
Chapter 7
Section
7.8
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Solutions 34 Videos

Which property of vectors is incorrect?

\displaystyle \mathbf{A} \quad \vec{a} \times \vec{b}=-\vec{b} \times \vec{a}

\displaystyle \mathbf{B} \quad \vec{a} \cdot(\vec{b}+\vec{c})=\vec{a} \cdot \vec{b}+\vec{a} \cdot \vec{c}

\displaystyle \mathbf{C} \quad (\vec{a}+\vec{b})+\vec{c}=\vec{a}+(\vec{b}+\vec{c})

\displaystyle \mathbf{D} \quad \vec{a} \cdot \vec{b}=\vec{a} \times \vec{b}

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Q2

Use the dot product to determine the total revenue from sales of 100 video game players at $399 and 240 DVD players at $129.

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Q8

Determine \vec{u} \times \vec{v} and \vec{u} \cdot \vec{v} for each pair of vectors.

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Q9a

Determine \vec{u} \times \vec{v} and \vec{u} \cdot \vec{v} for each pair of vectors.

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Q9b

Determine \vec{u} \times \vec{v} and \vec{u} \cdot \vec{v} for each pair of vectors.

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Q9c

Determine \vec{u} \times \vec{v} and \vec{u} \cdot \vec{v} for each pair of vectors.

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Q9d

a) Determine two unit vectors that are orthogonal to \vec{u}=[2,4,-9].

b) Explain why there is an infinite number of solutions to part \mathrm{a} ).

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Q12bc

Find the area of the parallelogram defined by each pair of vectors.

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Q15a

Find the area of the parallelogram defined by each pair of vectors.

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Q15b

A ramp is inclined at 12° to the horizontal. A cart is pulled 8 m up the ramp by a force of 120 N, at an angle of 10° to the surface of the ramp. Determine the mechanical work done against gravity. Would it be the same as the work done pulling the cart up the ramp? Explain.

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Q20

Resolve the vector \vec{v}=[7,9] into rectangular components, one of which is in the direction of

\displaystyle \vec{u}=[6,2]

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Q22

A parallelogram has an area of 200 cm^2. The side lengths are 90 cm and 30 cm. What are the measures of the angles?

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Q23

A box weighing 20 N, resting on a ramp, is kept at equilibrium by a 4—N force at an angle of 20° to the ramp, together with a frictional force of 5 N, parallel to the surface of the ramp. Determine the angle of elevation of the ramp.

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Q26