If #A= <2 ,1 ,-4 ># and #B= <3 ,2 ,7 >#, what is #A*B -||A|| ||B||#?

Answer 1
#A*B-|\|A|\||\|B|\|# is asking for the dot product of A and B and the product of the magnitudes of vectors A and B.
For the dot product, we find the sum of the products for the x, y, and z terms, so we find that: #A*B = (2*3)+(1*2)+(-4*7) = 6+2-28=-20#
For the magnitudes, we use the distance formula for 3D vectors: #d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)# or in this case, since the vectors already give the values of #x_2-x_1, y_2-y_1, z_2-z_1#, we simply plug in the given values: #|\|A|\| = sqrt(2^2+1^2+(-4)^2)=sqrt(21)# #|\|B|\| = sqrt(3^2+2^2+7^2)=sqrt(62)#
By putting all the parts together, we get: #A*B-|\|A|\||\|B|\|=-20-sqrt(21)*sqrt(62)=-20-sqrt(21*62)=-20-sqrt(1302)~~-56.083#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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