15 multiple choice questions covering vector notation, components, magnitude, dot product, projections, vector lines and applications.
Which quantity is a vector?
If $A(2, -1)$ and $B(5, 3)$, then vector $\vec{AB}$ is:
The magnitude of vector $(3, 4)$ is:
The unit vector in the direction of $(6, 8)$ is:
If $\vec{a} = (1, 2, -1)$ and $\vec{b} = (3, 0, 4)$, then $\vec{a} + \vec{b}$ is:
If $\vec{a} = (5, -2)$ and $\vec{b} = (1, 3)$, then $\vec{a} - \vec{b}$ is:
If $\vec{v} = (-2, 5)$, then $3\vec{v}$ is:
For $\vec{a} = (2, -1, 4)$ and $\vec{b} = (3, 5, -2)$, the dot product $\vec{a} \cdot \vec{b}$ is:
Two non-zero vectors are perpendicular when their dot product is:
The angle $\theta$ between non-zero vectors $\vec{a}$ and $\vec{b}$ satisfies:
The scalar projection of $\vec{a}$ onto $\vec{b}$ is:
A vector equation of a line through point $\vec{a}$ with direction vector $\vec{d}$ is:
Two vector lines with direction vectors $\vec{d_1}$ and $\vec{d_2}$ are parallel when:
For $\vec{r} = (1, 2, 3) + \lambda(2, -1, 4)$, a point on the line is:
For $\vec{r} = (1, 2, 3) + \lambda(2, -1, 4)$, a direction vector is: