7.8 Chapter Test
Chapter
Chapter 7
Section
7.8
Solutions 34 Videos Q1

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 Q5

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 Q10 Q11 Q12a

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 Q13 Q14

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 Q16 Q17 Q18 Q19

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] 

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?