Table of Contents
Ans. (c) (0, 1, 0)
Ans. (a) A pair of parallel planes
Explanation:
We know that the direction ratios of the line passing through two points katex is not definedare given by:
katex is not defined
Given points are A (2, 3, – 4), B (1, – 2, 3) and C (3, 8, – 11).
Direction ratios of the line joining A and B are:
1 – 2, – 2 – 3, 3 + 4
i.e. – 1, – 5, 7.
The direction ratios of the line joining B and C are:
3 –1, 8 + 2, – 11 – 3
i.e., 2, 10, – 14.
From the above, it is clear that direction ratios of AB and BC are proportional.
That means AB is parallel to BC. But point B is common to both AB and BC.
Hence, A, B, C are collinear points.
Explanation:
Given lines are:
katex is not defined
The direction ratios of the given lines are 7, -5, 1 and 1, 2, 3, respectively.
We know that,
Two lines with direction ratios katex is not defined are perpendicular to each other if katex is not defined
Therefore, 7(1) + (-5) (2) + 1 (3)
= 7 – 10 + 3
= 0
Hence, the given lines are perpendicular to each other.
Explanation:
Given plane is 2x + y – z = 5 ……(i)
Dividing both sides of the equation (i) by 5,
katex is not defined
We know that,
The equation of a plane in intercept form is katex is not defined where a, b, c are intercepts cut off by the plane at x, y, z-axes respectively.
For the given equation,
a = katex is not defined, b = 5, c = -5
Hence, the intercepts cut off by the plane are katex is not defined, 5 and -5.
Chapter No. | Chapter Name |
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Chapter 1 | Relations and Functions |
Chapter 2 | Inverse Trigonometric Functions |
Chapter 3 | Matrices |
Chapter 4 | Determinants |
Chapter 5 | Continuity and Differentiability |
Chapter 6 | Applications of Derivatives |
Chapter 7 | Integrals |
Chapter 8 | Applications of the Integrals |
Chapter 9 | Differential Equations |
Chapter 10 | Vectors |
Chapter 11 | Three - dimensional Geometry |
Chapter 12 | Linear Programming |
Chapter 13 | Probability |
Chapter Wise Important Questions for CBSE Board Class 12 Maths |
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Relations and Functions |
Inverse Trigonometric Functions |
Matrices |
Determinants |
Continuity and Differentiability |
Applications of Derivatives |
Integrals |
Applications of the Integrals |
Differential Equations |
Vectors |
Three - dimensional Geometry |
Linear Programming |
Probability |
CBSE Important Questions Class 10
ICSE Important Questions Class 10
CBSE Important Questions Class 10
ICSE Important Questions Class 10