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INTRODUCTION TO THREE DIMENSIONAL GEOMETRY MATHS - INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Gujarat Board (GSEB) - STD 11 Science - MATHS (GSEB - English Medium). 208 questions in this chapter.

Question types

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY question types

208 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

208
Questions
5
Question groups
5
Question types
Sample Questions

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY questions

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

Q 1MCQ1 Mark
If the distance between the points (a, 0, 1) and (0, 1, 2) is $\sqrt{27}$ then the value of a is:
  • A
    5
  • ✓
    $\underline{+}5$
  • C
    -5
  • D
    None of these

Answer: B.

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Q 2MCQ1 Mark
If A = (1, 2, 3), B = (2, 3, 4) and AB is produced upto C such that 2AB = BC then C =
  • A
    (5, 4, 6)
  • B
    (6, 2, 4)
  • ✓
    (4, 5, 6)
  • D
    (6, 4, 5)

Answer: C.

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Q 3MCQ1 Mark
There is one and only one sphere through:
  • ✓
    4 points not in the same plane
  • B
    4 points not lie in the same straight line
  • C
    None of these
  • D
    3 points not lie in the same line

Answer: A.

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Q 4MCQ1 Mark
The vector equation of a sphere having centre at origin and radius 5 is:
  • ✓
    $\mid{\text{r}}\mid = 5$
  • B
    $\mid{\text{r}}\mid = 25$
  • C
    $\mid{\text{r}}\mid = \sqrt{5}$
  • D
    None of these

Answer: A.

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Q 5MCQ1 Mark
The perpendicular distance of the point P(3, 3, 4) from the x-axis is
  • A
    $3\sqrt{2}$
  • ✓
    $5$
  • C
    $3$
  • D
    $4$

Answer: B.

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Q 11(Each question 2 marks)2 Marks
A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\left(\frac{8 k+2}{k+1}, \frac{-3}{k+1}, \frac{10 k+4}{k+1}\right)$].
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Q 24(Each question 4 marks)4 Marks
A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10). Find the coordinates of the point R. [Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\Big(\frac{8\text{k}+2}{\text{k}+1},\frac{-3}{\text{k}+1},\frac{10\text{k}+4}{\text{k}+1}\Big)]$
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