How do you normalize #<0, 1, 3>#?

Answer 1

#hatv = < 0, 1/(sqrt10), 3/(sqrt10) >#

Normalization of a vector is the process of finding a unit vector in the same direction of that vector (with magnitude (or "norm") #1#). It is found by the equation
#ulbar(|stackrel(" ")(" "hatv = (vecv)/(||vecv||)" ")|)#

where

#hatv# denotes the unit vector
#||vecv||# is the magnitude of vector #vecv#
The magnitude of #vecv# is given by
#||vecv|| = sqrt(0^2 + 1^2 + 3^2) = color(red)(ul(sqrt10#

Consequently, we have

#hatv = (< 0,1,3 >)/(color(red)(sqrt10)) = color(blue)(ulbar(|stackrel(" ")(" "< 0, 1/(sqrt10), 3/(sqrt10) >" ")|)#
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Answer 2
To normalize the vector <0, 1, 3>, you need to divide each component of the vector by its magnitude. The magnitude of a vector is calculated using the Euclidean norm formula: √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector. So, first, calculate the magnitude of the vector, and then divide each component by this magnitude to get the normalized vector.
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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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