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If vector a ,b and c are mutually perpendicula unit vector ,then find the value of |2a vector+ b vector+ c vector|

Posted by Rupa Borah 6 years, 11 months ago

CBSE > Class 12 > Mathematics

1 answers

Prangana Phukon 6 years, 11 months ago

Since a, b and c are mutually perpendicular unit vectors, we get a.b=0, b.c=0, a.c=0 and |a|= |b|=|c|=1 Also,|2a+b+c|2=(2a+b+c)⋅(2a+b+c) =2a⋅(2a+b+c)+b⋅(2a+b+c)+c⋅(2a+b+c) =4 a⋅a+2 a⋅b+2 a⋅c+2 b⋅a+ b⋅b+b⋅c+2 c⋅a+c⋅b+c⋅c a⋅a=|a|^2, b⋅b=|b|^2, c⋅c=|c|^2, and we know that dot product is commutative. So , |2a+b+c|2=4 |a|2+2a⋅b+2 a⋅c+2 a⋅b+|b|2+b⋅c+2a⋅c+b⋅c+|c|2 =4 |a|2+|b|2+|c|2+4 a⋅b+4 a⋅c+2 b⋅c =4(1)+1+1+4(0)+4 (0)c+2 (0) =6This further implies that, |2a+b+c| = √6

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