7.8 Chapter Test
Chapter
Chapter 7
Section
7.8
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} 

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.

Q8

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

Q9a

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

Q9b

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

Q9c

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

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}  ).

Q12bc

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

Q15a

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

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.

Q20

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

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

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?

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.