What is the projection of #<8,2,1 ># onto #<9,6,3 >#?

Answer 1

The answer is #=87/126〈9,6,3〉#

The vector projection of #vecb# onto #veca# is
#=(veca.vecb)/(∥veca∥^2)veca#
The dot product is #veca.vecb=〈8,2,1〉.〈9,6,3〉#
#=(72+12+3)=87#
The modulus of #veca# is #=∥veca∥=∥〈9,6,3〉∥#
#=sqrt(81+36+9)=sqrt126#
The vector projection is #=87/126〈9,6,3〉#
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Answer 2
To find the projection of vector A onto vector B, you can use the formula: Projection of A onto B = (A dot B) / (magnitude of B) * (unit vector of B) First, calculate the dot product of vectors A and B: A dot B = (8 * 9) + (2 * 6) + (1 * 3) = 72 + 12 + 3 = 87 Next, calculate the magnitude of vector B: |B| = sqrt((9^2) + (6^2) + (3^2)) = sqrt(81 + 36 + 9) = sqrt(126) = √126 Then, find the unit vector of vector B: Unit vector of B = B / |B| = <9/√126, 6/√126, 3/√126> Finally, plug the values into the formula to find the projection of vector A onto vector B: Projection of A onto B = (87) / (√126) * <9/√126, 6/√126, 3/√126> Projection of A onto B ≈ <5.036, 3.357, 1.679>
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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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