TS EAMCET · Maths · Three Dimensional Geometry
Consider the following
Assertion (A): The two lines \(\bar{r}=\bar{a}+t(\bar{b})\) and \(\bar{r}=\bar{b}+s(\bar{a})\) intersect each other.
Reason (R): The shortest distance between the lines \(\bar{r}=\bar{p}+t(\bar{q})\) and \(\bar{r}=\bar{c}+s(\bar{d})\) is equal to the length of projection of the vector \((\bar{p}-\bar{c})\) on \((\bar{q} \times \bar{d})\)
The correct answer is
- A Both (A) and (R) are true and (R) is the correct explanation of (A)
- B Both (A) and (R) are true and (R) is not the correct explanation of (A)
- C (A) is true, but (R) is false
- D (A) is false, but (R) is true
Answer & Solution
Correct Answer
(A) Both (A) and (R) are true and (R) is the correct explanation of (A)
Step-by-step Solution
Detailed explanation
Assertion (A): For intersection, \(\bar{a}+t\bar{b} = \bar{b}+s\bar{a} \implies (1-s)\bar{a} = (1-t)\bar{b}\). If \(\bar{a}\) and \(\bar{b}\) are non-collinear, then \(1-s=0\) and \(1-t=0 \implies s=1, t=1\). The lines intersect at \(\bar{a}+\bar{b}\). Thus (A) is true. Reason…
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