If #|hata-hatb|=sqrt2# then calculate the value of #|hata+sqrt3hatb|#?

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Answer 1 · 2017-05-29T14:08:21

#2#

#norm( hat a-hat b)^2=norm(hat a)^2-2 << hat a, hat b >> + norm(hat b)^2 =1-2 << hat a, hat b >>+1 = (sqrt2)^2=2#

so #<< hat a, hat b >> = 0# the unit vectors are orthogonal.

Now

#norm( hat a+sqrt3 hat b)^2 = norm( hat a)^2+2 sqrt3 << hat a, hat b >> + 3 norm(hat b)^2 = 1+2sqrt3 xx 0+3 = 4#

so

#norm( hat a+sqrt3 hat b)=sqrt(4)=2#

NOTE: #<< cdot, cdot >># indicates the scalar product of two vectors.