Maths · Scalar and vector products
Assertion In each of the three planes determined by two of the lines ( being the
Assertion In each of the three planes determined by two of the lines \( O A, O B, O C \) ( \( O \) being the origin), a straight line is drawn through \( O \) perpendicular to the third line. The three lines so determined are coplanar. Reason \( (a \times b) \times c+(b \times c) \times a+(c \times a) \times \) \( b=0, \) where \( O A=a, O B=b \) and \( \boldsymbol{O} \boldsymbol{C}=\boldsymbol{c} \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Both Assertion and Reason are incorrect
Step-by-step solution
The lines are along vectors (a×b)×c, (b×c)×a, (c×a)×b. The given identity shows their sum is zero, implying they are coplanar, thus the lines are coplanar. The reason correctly explains the assertion.
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