InterviewSolution
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InterviewSolution
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What is the angle between the following pair of vectors? `vec(A)=hat(i)+hat(j)+hat(k)` and `vec(B)=-2hat(i)-2hat(j)-2hat(k)`. |
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Answer» `vec(A).vec(B)=ABcos theta` or `cos theta=(vec(A)vec(B))/(AB)`….(i) But, `vec(A).vec(B)=(hat(i)+hat(j)+hat(k)).(-2hat(i)-2hat(j)-2hat(k))` `vec(A).vec(B)=-2-2-2=-6` Again `A=|vec(A)|=sqrt((1)^(2)+(1)^(2)+(1)^(2))=sqrt(3),` `B=|vec(B)|=sqrt((-2)^(2)+(-2)^(2)+(-2)^(2))=sqrt(12)=2sqrt(3)` Now, `cos theta=(-6)/(sqrt(3)xx2sqrt(3))=-1 rArr theta=180^(@)` |
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