Vector Algebra — Course Quiz | Expresswala Academy

Ten questions on vectors, components, the section formula and scalar and vector products. Pick one answer for each.

10 questions, one mark each. 6 to pass. Suggested time: 20 minutes. Your answers are not recorded.

Find $\lvert\hat i + 2\hat j + 2\hat k\rvert$ .

A $\sqrt{5}$

B $3$

C $9$

D $5$
The unit vector along $6\hat i + 8\hat k$ is

A $6\hat i + 8\hat k$

B $0.6\hat i + 0.8\hat k$

C $0.6\hat i + 0.8\hat j$

D $\displaystyle \tfrac{3}{7}\hat i + \tfrac{4}{7}\hat k$
Which vector is collinear with $\hat i - 2\hat j + 3\hat k$ ?

A $-\hat i - 2\hat j - 3\hat k$

B $2\hat i + 4\hat j + 6\hat k$

C $-2\hat i + 4\hat j - 6\hat k$

D $3\hat i - 2\hat j + \hat k$
The midpoint of the points with position vectors $2\hat i + 4\hat j - \hat k$ and $4\hat i + 3\hat k$ is

A $\hat i - 2\hat j + 2\hat k$

B $3\hat i + 2\hat j + \hat k$

C $3\hat i + 2\hat j + 2\hat k$

D $6\hat i + 4\hat j + 2\hat k$
Which triple can be the direction cosines of a line?

A $\displaystyle \tfrac{1}{3}, \tfrac{2}{3}, \tfrac{1}{3}$

B $\displaystyle \tfrac{1}{\sqrt{3}}, \tfrac{1}{\sqrt{3}}, \tfrac{1}{\sqrt{3}}$

C $1, 1, 0$

D $\displaystyle \tfrac{1}{2}, \tfrac{1}{2}, \tfrac{1}{2}$
Find the angle between $\hat i + \hat j$ and $\hat j + \hat k$ .

A $90^\circ$

B $45^\circ$

C $60^\circ$

D $120^\circ$
If $\lvert\vec a\rvert = 2$ , $\lvert\vec b\rvert = 5$ and $\vec a \cdot \vec b = 5$ , the angle between $\vec a$ and $\vec b$ is

A $60^\circ$

B $45^\circ$

C $90^\circ$

D $30^\circ$
For any vector $\vec a$ , $\vec a \times \vec a$ equals

A $\vec a$

B $\vec 0$

C $1$

D $\lvert\vec a\rvert^2$
$\hat j \times \hat i$ equals

A $-\hat k$

B $1$

C $\hat k$

D $\vec 0$
For a triangle $ABC$ with $\overrightarrow{AB} = 2\hat i$ and $\overrightarrow{AC} = 3\hat j$ , the area is

A $5$

B $3$

C $\displaystyle \tfrac{5}{2}$

D $6$

Unanswered questions are marked wrong.

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Vector Algebra — Course Quiz

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