Maths-
General
Easy

Question

If a, b, c are non-coplanar unit vectors such that a × (b × c) = fraction numerator b plus c over denominator square root of 2 end fraction, then the angle between a and b is -

  1. 3/4  
  2. /4  
  3. /2  
  4.   

The correct answer is: 3/4


    The given equality implies
    (a . c) b – (a . b) c = fraction numerator b plus c over denominator square root of 2 end fraction
    open parentheses a. c – fraction numerator 1 over denominator square root of 2 end fraction close parentheses b = open parentheses fraction numerator 1 over denominator square root of 2 end fraction plus a. b close parenthesesc
     b and c are collinear thus a, b, c are coplanar if a . c  fraction numerator 1 over denominator square root of 2 end fractionand a . b  – fraction numerator 1 over denominator square root of 2 end fraction. Hence a . b = – fraction numerator 1 over denominator square root of 2 end fraction  cos  = –1/square root of 2, where  is the angle between a and b. So  = 3/4.

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