3.13 Scalar and vector products Quiz

1. Which statement is true about $(2,-3,1)$ and $(4,1,-5)$?

• A. They are parallel.
• B. They meet at an acute angle.
• C. They are perpendicular.
• D. They meet at an obtuse angle.

2. Find the angle between $(1,0)$ and $(1,1)$.

• A. $45^\circ$
• B. $60^\circ$
• C. $30^\circ$
• D. $90^\circ$

3. Find $\mathbf{i}\times\mathbf{j}$, where $\mathbf{i}=(1,0,0)$ and $\mathbf{j}=(0,1,0)$.

• A. $(0,0,-1)$
• B. $(0,0,0)$
• C. $(1,1,0)$
• D. $(0,0,1)$

4. In triangle $ABC$, $\overrightarrow{AB}=(2,0,0)$ and $\overrightarrow{AC}=(0,3,0)$. Find its area.

• A. $6$
• B. $3$
• C. $9$
• D. $5$

5. Find the component of $\mathbf{a}=(3,4)$ in the direction of $\mathbf{b}=(0,5)$.

• A. $20$
• B. $5$
• C. $4$
• D. $3$