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Direction Cosines and Direction Ratios Maths - Direction Cosines and Direction Ratios

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - 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
If O is the origin, OP = 3 with direction ratios proportional to -1, 2, -2 then the coordinates of P are:
  1. $(-1, 2,-2)$
  2. $(1, 2, 2)$
  3. $\Big(\frac{-1}{9},\frac{2}{9},\frac{-2}{9}\Big)$
  4. $(3,6,-9)$
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Q 2M.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:
  1. $\Big(\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
  2. $\Big(-\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
  3. $\Big(\frac{19}{8},-\frac{57}{16},\frac{17}{16}\Big)$
  4. $\text{none of these}$
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Q 3M.C.Q (1 Marks)1 Mark
A parallelopiped is formed by planes drawn through the point (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes. The length of a diagonal of the parallelopiped is:
  1. $7$
  2. $\sqrt{38}$
  3. $\sqrt{155}$
  4. $\text{none of these}$
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Q 4M.C.Q (1 Marks)1 Mark
Ratio in which the xy-plane divided the join of (1, 2, 3) and (4, 2, 1) is:
  1. 3 : 1 internally
  2. 3 : 1 externally
  3. 2 : 1 internally
  4. 2 : 1 externally
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Q 5M.C.Q (1 Marks)1 Mark
The distance of the point P(a, b, c) from the x-axis is:
  1. $\sqrt{\text{b}^2+\text{c}^2}$
  2. $\sqrt{\text{a}^2+\text{c}^2}$
  3. $\sqrt{\text{a}^2+\text{b}^2}$
  4. $\text{none of these}$
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Q 113 Marks3 Marks
Show that the line through points (1, -1, 2) and (3, 4, -2) is perpendicular to the line throught the points (0, 3, 2) and (3, 5, 6).
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Q 133 Marks3 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 143 Marks3 Marks
Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line throught the points (-1, -2, 1) and (1, 2, 5).
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Q 174 Marks4 Marks
Find the angle between the lines whose direction cosines are given by the equations:
l + m +n = 0 and l2 + m2 + n2 = 0
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Q 194 Marks4 Marks
Find the angle between the lines whose direction cosines are given by the equations:
2l - m + 2n = 0 and mn + nl + lm = 0
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