Maharashtra State BoardHSC Arts 12th Board Exam
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If c¯=3a¯-2b¯ then prove that [a¯b¯c¯] = 0 - Mathematics and Statistics

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Sum

If `bar("c") = 3bar("a") - 2bar("b")` then prove that `[(bar("a"), bar("b"), bar("c"))]` = 0

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Solution

`bar("c") = 3bar("a") - 2bar("b")`    .......[Given]

`[(bar("a"), bar("b"), bar("c"))] = bar("a")*(bar("b") xx bar("c"))`

= `bar("a")*[bar("b") xx (3bar("a") - 2bar("b"))]`

= `bar("a")*[bar("b") xx 3bar("a") - bar("b") xx 2bar("b")]`

= `bar("a")*[bar("b") xx 3bar("a") - bar(0)]`    .......`[∵  bar("b") xx bar("b") = bar(0)]`

= `3bar("a")*[bar("b") xx bar("a")]`

= `3[(bar("a"), bar("b"), bar("a"))]`

= 3(0)

∴ `[(bar("a"), bar("b"), bar("a"))]` = 0

Concept: Vector Joining Two Points
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