Three Dimensional Geometry — Course Quiz

Ten questions on direction cosines, equations of lines, angles and shortest distances in space. Pick one answer for each.

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

A line makes equal angles with all three axes. Its direction cosines are

A $\displaystyle \tfrac{1}{3}$ each

B $\displaystyle \pm\tfrac{1}{\sqrt{3}}$ each

C $1$ each

D $\displaystyle \pm\tfrac{1}{\sqrt{2}}$ each
The direction ratios of the line $\displaystyle \dfrac{x - 1}{2} = \dfrac{y + 3}{-1} = \dfrac{z}{5}$ are

A $1, -3, 0$

B $2, 1, 5$

C $2, -1, 5$

D $-1, 3, 0$
Which point lies on the line $\displaystyle \dfrac{x - 3}{2} = \dfrac{y + 1}{4} = \dfrac{z - 2}{-1}$ ?

A $(3, 1, 2)$

B $(-3, 1, -2)$

C $(3, -1, 2)$

D $(2, 4, -1)$
The direction ratios of the line $\displaystyle \dfrac{x - 1}{2} = \dfrac{3 - y}{4} = \dfrac{z + 2}{1}$ are

A $2, 4, 1$

B $2, -4, 1$

C $1, 3, -2$

D $2, 4, -1$
The vector equation of the line through $(1, 0, 2)$ parallel to $\hat i - \hat j + 3\hat k$ is

A $\vec r = \hat i + 2\hat j + \lambda(\hat i - \hat j + 3\hat k)$

B $\vec r = \hat i - \hat j + 3\hat k + \lambda(\hat i + 2\hat k)$

C $\vec r = \lambda(\hat i + 2\hat k)$

D $\vec r = \hat i + 2\hat k + \lambda(\hat i - \hat j + 3\hat k)$
The angle between lines with direction ratios $1, 2, 2$ and $2, 1, -2$ is

A $60^\circ$

B $45^\circ$

C $0^\circ$

D $90^\circ$
The points $A(1, 2, 3)$ , $B(2, 4, 5)$ and $C(4, 8, 9)$ are

A not collinear, since $AB \ne BC$

B collinear

C vertices of an equilateral triangle

D vertices of a right-angled triangle
Find the shortest distance between $\vec r = \lambda\hat k$ and $\vec r = \hat i + \mu\hat j$ .

A $0$

B $2$

C $1$

D $\sqrt{2}$
Find the distance between the parallel lines $\vec r = \lambda\hat i$ and $\vec r = 2\hat j + \mu\hat i$ .

A $1$

B $2$

C $4$

D $\sqrt{2}$
The direction cosines of the line through the origin and $(2, 3, 6)$ are

A $\displaystyle \tfrac{2}{49}, \tfrac{3}{49}, \tfrac{6}{49}$

B $\displaystyle \tfrac{2}{7}, \tfrac{3}{7}, \tfrac{6}{7}$

C $2, 3, 6$

D $\displaystyle \tfrac{2}{11}, \tfrac{3}{11}, \tfrac{6}{11}$

Unanswered questions are marked wrong.

Menu

Three Dimensional Geometry — Course Quiz

More practice