What is the norm of <1,-3,-2 ><1,−3,−2>?

1 Answer
Truong-Son N.
Apr 1, 2016

Let vecv = << 1,-3,-2 >>→v=⟨1,−3,−2⟩. The norm is written as

\mathbf(|| vecv || = sqrt(vecvcdotvecv))

= sqrt(<< 1,-3,-2 >>cdot<< 1,-3,-2 >>)

= sqrt(1cdot1 + (-3)cdot(-3) + (-2)cdot(-2))

= sqrt(1^2 + (-3)^2 + (-2)^2)

= sqrt(1 + 9 + 4)

= color(blue)(sqrt(13))

This tells us that the vector has a length of sqrt(13) ~~ 3.61. In fact, this is really a generalization of the Pythagorean Theorem in RR^3.

Given that information, can you find the norm of vecw = << 1, 3, -2, 7 >>?

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