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If a b c ≠0 then a . p + b . q+c. r is equal to - Mathematics and Statistics

MCQ
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If`[ bara  bar b barc ] ≠ 0  and  barp = [ barb xx barc ]/([ bara  bar b barc  ]), barq = [ barc xx bara ]/([ bara  bar b barc  ]), barr = [ bara xx barb ]/[ bara  bar b barc ]`

then `bara . barp + barb . barq + barc . barr` is equal to ______.

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Solution

(d) 3

Given

`bar p=(barbxxbarc)/([bara barb barc])`

`bar q=(barcxxbara)/([bara barb barc])`

`bar r=(baraxxbarb)/([bara barb barc])`

`=bar a . barp +bar b . bar q+bar c. bar r`

`=bar a.(barbxxbarc)/([bara barb barc])+bar b.(barcxxbara)/([bara barb barc])+barc.(baraxxbarb)/([bara barb barc]) ............. [because[bara barb barc]=bara.(barbxxbarc)]`

=

`([bara barb barc])/([bara barb barc])+([bara barb barc])/([bara barb barc])+([bara barb barc])/([bara barb barc])`

`=3([bara barb barc])/([bara barb barc])`

=3

Concept: Vectors - Linear Combination of Vectors
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