6. Advanced Topics

Vectors — Quiz

Test your understanding of vectors with 5 practice questions.

Practice Questions

Question 1

Given vectors $\mathbf{u}=\langle2,1\rangle$ and $\mathbf{v}=\langle1,3\rangle$, find scalars $a$ and $b$ such that $\mathbf{w}=\langle7,10\rangle=a\mathbf{u}+b\mathbf{v}$. What are $a$ and $b$?

Question 2

What is the area of the triangle with vertices $A(1,2)$, $B(4,6)$, and $C(-1,5)$?

Question 3

Lines $r_1(t)=\langle2,-1\rangle+t\langle3,4\rangle$ and $r_2(s)=\langle5,3\rangle+s\langle-1,2\rangle$ intersect at which point?

Question 4

For which value of $x$ are the vectors $\langle4,-2\rangle$ and $\langle x,5\rangle$ parallel?

Question 5

A boat sails $20\,$km at $30^\circ$ north of east, then $15\,$km at $120^\circ$ from the positive $x$-axis. What is the magnitude and direction (north of east) of the resultant displacement?