What is the projection of #<-5,2,8># onto #<8,-3,3 >#?

Answer 1

#vec C=-11/41(8 hat i-3 hat j+3 hat k)#

#vec A=-5 hat i+2 hat j+8 hat k" "vec B=8 hat i-3 hat j+3 hat k# #A*B=-5*8+2(-3)+8*3=-40-6+24=-22# #||B||=sqrt(8^2+(-3)^2+3^2)=sqrt(64+9+9)=sqrt82# #"the projection of "vec A " onto "vec B" is given: " vec C=(vec A*vec B)/||B||^2 vec B# #vec C=-22/(sqrt82)^2(8 hat i-3 hat j+3 hat k)# #vec C=-22/82(8 hat i-3 hat j+3 hat k)# #vec C=-11/41(8 hat i-3 hat j+3 hat k)#

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Answer 2

Lily Adams

To find the projection of vector \( \vec{a} \) onto vector \( \vec{b} \), you can use the formula: \[ \text{proj}_{\vec{b}}(\vec{a}) = \frac{\vec{a} \cdot \vec{b}}{\| \vec{b} \|^2} \cdot \vec{b} \] Given \( \vec{a} = <-5, 2, 8> \) and \( \vec{b} = <8, -3, 3> \): 1. Calculate the dot product of \( \vec{a} \) and \( \vec{b} \). 2. Calculate the magnitude squared of \( \vec{b} \). 3. Plug the values into the formula and compute the projection.

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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 projection of #&lt;-5,2,8&gt;# onto #&lt;8,-3,3 &gt;#?

What is the projection of #<-5,2,8># onto #<8,-3,3 >#?