Maharashtra State BoardHSC Arts 12th Board Exam
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If bar"a", bar"b", bar"c" are three non-coplanar vectors show that (bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b") = 0 - Mathematics and Statistics

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Sum

If `bar"a", bar"b", bar"c"` are three non-coplanar vectors show that `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b") = 0`

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Solution

LHS = `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b")`

`= [(bar"a" bar"b" bar"c")]/[(bar"c"bar"a"bar"b")] + [(bar"b" bar"a" bar"c")]/[(bar"c" bar"a" bar"b")]`

`= [(bar"a"  bar"b"  bar"c")]/[(bar"a"  bar"b"  bar"c")] - [(bar"a"  bar"b"  bar"c")]/[(bar"a"  bar"b"  bar"c")]`

= 0 = RHS.

Concept: Vectors and Their Types
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