Question
If the angle θ between the vectors a=2x2^i+4x^j+^k and b=7^i−2^j+x^k is such that 90∘ < θ < 180∘
then x lies in the interval:
then x lies in the interval:
Answer: Option A
:
A
90∘<θ<180∘⇒a.b<0⇒(2x2^i+4x^j+^k).(7^i−2^j+x^k)<0⇒14x2−8x+x<0⇒14x2−7x<0⇒7x(2x−1)<0⇒0<x<12
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:
A
90∘<θ<180∘⇒a.b<0⇒(2x2^i+4x^j+^k).(7^i−2^j+x^k)<0⇒14x2−8x+x<0⇒14x2−7x<0⇒7x(2x−1)<0⇒0<x<12
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