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What is the angle between #<5 , 5 , -1 > # and # < 4, -3 , 1 > #?

Answer 1

Elijah Alexander

#hat(vec u,vec v) = 1.46073# [rad] #approx 83.70^@#

Given two vectors #vec u, vec v# we know that

#<< vec u, vec v >> = norm(vec u) xx norm(vec v) xx cos(hat(vec u,vec v))#

Solving for the angle #hat(vec u,vec v)# we have

#hat(vec u,vec v) = arccos(<< vec u, vec v >>/(norm(vec u) xx norm(vec v)))#

In our example

#vec u = {5,5,-1}# #vec v = {4,-3,1}#

#<< vec u, vec v >> =5 xx 4+5 xx (-3)+(-1)xx1 = 4# #norm vec u = sqrt(5^2+5^2+(-1)^2) = sqrt(51)# #norm vec v = sqrt(4^2+(-3)^2+1^2) = sqrt(26)#

then

#hat(vec u,vec v) = arccos(4/sqrt(51 xx 26)) = 1.46073# [rad] #approx 83.70^@#

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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.

What is the angle between #&lt;5 , 5 , -1 &gt; # and # &lt; 4, -3 , 1 &gt; #?

What is the angle between #<5 , 5 , -1 > # and # < 4, -3 , 1 > #?