Given `vec(A)=4hat(i)+6hat(j)` and `vec(B)=2hat(i)+3hat(j)`. Which of the followingA. `vec(A)xxvec(B)=vec(0)`B. `vec(A).vec(B)=24`C. `(|vec(A)|)/(|vec(B)|)=1/2`D. `vec(A)` and `vec(B)` are antiparallel

Given `vec(A)=4hat(i)+6hat(j)` and `vec(B)=2hat(i)+3hat(j)`. Which of

1.	Given `vec(A)=4hat(i)+6hat(j)` and `vec(B)=2hat(i)+3hat(j)`. Which of the followingA. `vec(A)xxvec(B)=vec(0)`B. `vec(A).vec(B)=24`C. `(\|vec(A)\|)/(\|vec(B)\|)=1/2`D. `vec(A)` and `vec(B)` are antiparallel
Answer» Correct Answer - A `vec(A)xxvec(B)=(4hat(i)+6hat(j))xx(2hat(i)+3hat(j))=12(hat(i)xxhat(j))+12(hat(j)xxhat(i))` `=12(hat(i)xxhat(j))-12(hat(i)xxhat(j))=0` Again, `vec(A).vec(B)=(4hat(i)+6hat(j)).(2hat(i)+3hat(j))=8+18=26` Again`(\|vec(A)\|)/(\|vec(B)\|)=(sqrt(16+36))/(sqrt(4+9))!=1/2` Also, `vec(B)=1/2vec(A) rArr vec(A)` and `vec(B)` are parallel and not antiparallel.

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