What is # || < 5 , -6 , 9> + < 2 , -4, -7 > || #?

1 Answer
May 24, 2017

Answer:

# 3sqrt(17) #

Explanation:

First, let us calculate the vector sum:

Let #vec(u) \ =<< 5 , -6 , 9>>#
And #vec(v)=<< 2 , -4, -7 >>#

Then:

# vec(u) + vec(v) = << 5 , -6 , 9>> + << 2 , -4, -7 >>#
# " " = << (5)+(2) , (-6)+(-4) , (9)+(-7)>>#
# " " = << 7 , -10 , 2>>#

So then the metric norm is:

# || vec(u) + vec(v) || = || << 7 , -10 , 2>> || #
# " " = sqrt((7)^2 + (-10)^2 + (2)^2 ) #
# " " = sqrt( 49 + 100 + 4 ) #
# " " = sqrt( 153 ) #
# " " = 3sqrt(17) #