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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

Paragraph: The position vectors of two points A and B are i - j and...

Paragraph: The position vectors of two points A and B are i^−j^\hat{i}-\hat{j} and j^+k^\hat{j}+\hat{k} respectively.
Question: Consider the following points: 1. (−1,−3,1)2.(-1,-3,1) 2.(-1,3,2)3.3.(-2,5,3)WhichoftheabovepointslieonthelinejoiningWhich of the above points lie on the line joiningAandandB??

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

B. 2 and 3 only

Step-by-step solution

A(i^−j^)A(\hat{i}-\hat{j}) and B(j^+k^)B(\hat{j}+\hat{k}) Equation of AB→=(j^+k^)−(i^−j^)=−i^+2j^+k^∴\overrightarrow{A B}=(\hat{j}+\hat{k})-(\hat{i}-\hat{j})=-\hat{i}+2 \hat{j}+\hat{k}\therefore \quad Direction ratio of line parallel to AB=(−1,2,1)A B=(-1,2,1). ∴\therefore \quad Equation of line passing through AA and pass through AB,x−1−1=y+12=z−01A B, \frac{x-1}{-1}=\frac{y+1}{2}=\frac{z-0}{1} Clearly (−1,3,2)(-1,3,2) and (−2,5,3)(-2,5,3) is satisfying i.e. only 2 and 3.
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