📐 Vectors and Geometric Problems

Questions in this quiz

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1. Question 1

   If vector $\vec{a} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, what is its magnitude?

2. Question 2

   Two vectors are perpendicular if and only if their dot product equals zero.

3. Question 3

   The dot product of $\vec{p} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$ and $\vec{q} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ is ___.

4. Question 4

   Which of the following represents a vector parallel to $\vec{v} = \begin{pmatrix} 2 \\ -3 \end{pmatrix}$?

5. Question 5

   The position vector of the midpoint of a line segment joining points $A$ and $B$ is $\frac{1}{2}(\vec{a} + \vec{b})$.

6. Question 6

   Given vectors $\vec{u} = \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}$ and $\vec{v} = \begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}$, calculate $\vec{u} \cdot \vec{v}$.

7. Question 7

   If a straight line passes through point $(2, 3)$ in direction of vector $\begin{pmatrix} 1 \\ -2 \end{pmatrix}$, the parametric equation is $x = 2 + t$ and y = ___ + ___t.

8. Question 8

   If $\vec{a} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ and $\vec{b} = \begin{pmatrix} 6 \\ 8 \end{pmatrix}$, then the angle between them is $0°$.

9. Question 9

   Three points are collinear if and only if the vectors formed by them are:

10. Question 10

    Arrange these steps in the correct order to find the angle between two vectors $\vec{u}$ and $\vec{v}$.