How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = -i - 2k and B = - 5i + 5j + 5k?

Answer 1

The angle is #=105º#

The dot product of #vecA# and #vecB# is given by #vecA.vecB=∥vecA∥.∥vecB∥costheta# where #theta# is the angle between the 2 vectors. Here, #vecA=〈-1,0,-2〉# and #vecB=〈-5,5,5〉#
The dot product #vecA.vecB=〈-1,0,-2〉.〈-5,5,5〉=5+0-10=-5#
The modulus of #vecA=∥〈-1,0,-2〉∥=sqrt(1+0+4)=sqrt5#
The modulus of #vecB=∥〈-5,5,5〉∥=sqrt(25+25+25)=sqrt75#
#cos theta=(vecA.vecB)/(∥vecA∥.∥vecB∥)=-5/(sqrt5*sqrt75)=-1/sqrt15=-0.258#
#theta=105º#
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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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