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How do you normalize #(- 4i + 5 j- k)#?

Answer 1

Nathan Ashcroft

# -4/sqrt(42)hati+5/ sqrt(42)hatj-1/ sqrt(42)hatk#

A vector can be normalised by dividing it by its metric norm, resulting in a new scaled vector with a norm of unity.

Let me

# vec u = -4hati+5hatj-hatk#

The metric norm is thus provided by:

# || bar u || ^2 = (-4)^2+(5)^2+(-1)^2 # # " " = 16+25+1 # # " " = 42 # # :. || bar u || = sqrt(42) #

Thus,

# hatbaru = (baru) / (|| bar u ||) # # \ \ = (baru) / sqrt(42) # # \ \ = 1 / sqrt(42) (-4hati+5hatj-hatk# # \ \ = -4/ sqrt(42)hati+5/ sqrt(42)hatj-1/ sqrt(42)hatk#

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Answer 2

Elena Albarran

To normalize the vector (-4i + 5j - k), first calculate its magnitude using the formula |v| = sqrt(a^2 + b^2 + c^2), where a, b, and c are the components of the vector. Then divide each component of the vector by its magnitude to obtain 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.