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Motion in A Plane question

2013 · Q146
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  5. /2013 · Q146

Motion in A Plane question

2013 · Q146

NEETPhysicsMotion in A PlaneMCQ+4 / −1
Vectors A→,B→\overrightarrow A ,\overrightarrow BA,B and C→\overrightarrow CC are such that A→.B→=0\overrightarrow A .\overrightarrow B = 0A.B=0 and A→.C→=0\overrightarrow A .\overrightarrow C = 0A.C=0. Then the vector parallel to A→\overrightarrow AA is
  1. A
    A→×B→\overrightarrow A \times \overrightarrow BA×B
  2. B
    B→+C→\overrightarrow B + \overrightarrow CB+C
  3. C
    B→×C→\overrightarrow B \times \overrightarrow CB×C
  4. D
    B→\overrightarrow BB and C→\overrightarrow CC
View written solutionFree

Correct answer: C

Vector triple product of three vectors A→\overrightarrow A A, B→\overrightarrow B B and C→\overrightarrow C C is

A→×(B→×C→)=(A→.C→)B→−(A→.B→)C→\overrightarrow A \times \left( {\overrightarrow B \times \overrightarrow C } \right) = \left( {\overrightarrow A .\overrightarrow C } \right)\overrightarrow B - \left( {\overrightarrow A .\overrightarrow B } \right)\overrightarrow C A×(B×C)=(A.C)B−(A.B)C

Given: A→.B→=0,A→.C→=0\overrightarrow A .\overrightarrow B = 0,\overrightarrow A .\overrightarrow C = 0A.B=0,A.C=0
\therefore $$$\overrightarrow A \times \left( {\overrightarrow B \times \overrightarrow C } \right) = 0$$<br><br> Thus the vector\overrightarrow A $ is parallel to vector B→×C→{\overrightarrow B \times \overrightarrow C }B×C .

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