Assertion (A) : For the lines \overline{ {\r}}=\overline{ {\a}}+ {\t} \overline{ {\b}} and \overline{ {\r}}=\overline{ {\p}}+ { s} \overline{ {\q}}, if (\overline{a}-\overline{p}) \cdot(\overline{b} \times \overline{q}) \neq 0, then the two lines are coplanar Reason (R) : |(\overline{ {\a}}-\overline{ {\p}}) \cdot(\overline{ {\b}} \times \overline{ {\q}})| is |\overline{ {\b}} \times \overline{ {\q}}| times the shortest distance between the lines \overline{ {\r}}=\overline{ {\a}}+ {\t} \overline{ {\b}} and \overline{ {\r}}=\overline{ {\p}}+ { s} \overline{ {\q}}. [AP EAPCET 24 May 2025 S1]

Correct Answer is : (A) is false, (R) is true

(A) is true, (R) is true and (R) is correct explanation to (A)

(A) is true, (R) is true and (R) is not the correct explanation to (A)

Three Dimensional Geometry

Section: Mathematics

Question : 7 of 58

Marks: +1, -0

Assertion (A) : For the lines r=a+tb and r=p+ sq, if (a−p)⋅(b×q)≠0, then the two lines are coplanar
Reason (R) : ‌‌|(a−p)⋅(b×q)| is |b×q| times the shortest distance between the lines r=a+tb and r=p+ sq.

[AP EAPCET 24 May 2025 S1]

(A) is true, (R) is true and (R) is correct explanation to (A)
(A) is true, (R) is true and (R) is not the correct explanation to (A)
(A) is true, (R) is false
(A) is false, (R) is true

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