87959 If c→=3a→−2b→, then the value of a→⋅(b→×c→)=
(B)Given,c→=3a→−2b→a→⋅(b→×c→)=?a→⋅(b→×c→)=a→⋅[b→×(3a→−2b→)]=a→⋅(3a→×b→−2b→×b→)=a→⋅(3a→×b→−0→)=3a→⋅(b→×a→)=3(0)=0∵(b→×b→=0)
88097 If |a|=2,|b|=5 and |a×b|=8, then |a.b| is equal to
(A) : Given,|a→|=2|b→|=5(a→×b→)=8|a×b|=|a||b|sinθ=82.5⋅sinθ=8sinθ=45cosθ=35a⋅b=|a||b|cosθ=2×5×35or |a→⋅b→|=±6
87968 If a→⋅b→=−|a→||b→|, then the angle between a→ and b→ is
(D) : Given,a→⋅b→=−|a→||b→|The angle between a→ and b→a→⋅b→=|a→||b→|cosθ|a→||b→|cosθ=−|a→||b→|[∵|a→|≠0,|b→|≠0]cosθ=−1θ=180∘
88098 a,b,c are three vectors such that a+b+c=0, |a|=1,|b|=2,|c|=3, then a.b+b.c+c.a is equal to
(B) : Given that, |a→|=1,|b→|=2,|c→|=3Anda→+b→+c→=0(a→+b→+c→)2=|a→|2+|b→|2+|c→|2+(a→⋅b→+b→⋅c→+c→⋅a→)0⇒12+22+33+2(a→⋅b→+b→⋅c→+c→⋅a→)⇒2(a→⋅b→+b→⋅c→+c→⋅a→)=−14⇒a→⋅b→+b→⋅c→+c→⋅a→=−7
88119 For any vector a→ the value of (a→×i)2+(a→×j^)2+(a→×k^)2 is equal to
(C) : Let,a→=xi^+yk^+zk^⇒a→×i^=zj^−yk^(a→×i^)2=y2+z2Similarly (a→×j^)=x2+z2and (a→×k^)2=x2+y2∴(a→×i^)2+(a→×j^)+(a→×k^)2=2(x2+y2+z2)=2a→2