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Direction Cosines and Direction Ratios MATHS - Direction Cosines and Direction Ratios

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 53 questions in this chapter.

Question types

Direction Cosines and Direction Ratios question types

53 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

53
Questions
4
Question groups
5
Question types
Sample Questions

Direction Cosines and Direction Ratios questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The xy-plane divided the line joining the point (-1, 3, 4) and (2, -5, 6)
  • A
    Internally in the ratio 2 : 3
  • ✓
    Externally in the ratio 2 : 3
  • C
    Internally in the ratio 3 : 2
  • D
    Externally in the ratio 3 : 2

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
For every point P(x, y, z) on the x-axis (except the origin),
  • A
    x = 0, y = 0, z ≠ 0
  • B
    y = 0, z = 0, y ≠ 0
  • ✓
    y = 0, z = 0, x ≠ 0
  • D
    x = y = z = 0

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark
If O is the origin, OP = 3 with direction ratios proportional to -1, 2, -2 then the coordinates of P are:
  • ✓
    $(-1, 2,-2)$
  • B
    $(1, 2, 2)$
  • C
    $\Big(\frac{-1}{9},\frac{2}{9},\frac{-2}{9}\Big)$
  • D
    $(3,6,-9)$

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark
A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3) are the vertices of a tringle ABC. if the bisector of $\angle\text{ABC}$ meets BC at D, then coordinates of D are:
  • ✓
    $\Big(\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
  • B
    $\Big(-\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
  • C
    $\Big(\frac{19}{8},-\frac{57}{16},\frac{17}{16}\Big)$
  • D
    $\text{none of these}$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark
Ratio in which the xy-plane divided the join of (1, 2, 3) and (4, 2, 1) is:
  • A
    3 : 1 internally
  • ✓
    3 : 1 externally
  • C
    2 : 1 internally
  • D
    2 : 1 externally

Answer: B.

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Q 123 Marks Question3 Marks
Show that the line joining the origin to the point $(2, 1, 1)$ is perpendicular to the line determined by the points $(3, 5, -1)$ and $(4, 3, -1).$
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Q 153 Marks Question3 Marks
If a unit vector $\vec{\text{a}}$ makes an angle $\frac{\pi}{3}$ with $\hat{\text{i}},\frac{\pi}{4}$ with $\hat{\text{j}}$ and an acute angle $\theta$ with $\hat{\text{k}}$, and ,then find the value of $\theta$.
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