What is # || + || #?

Question

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

Charles Aeschliman · Accepted Answer

# 3sqrt(17) #

Let's compute the vector sum first: Let #vec(u) \ =<< 5 , -6 , 9>># And #vec(v)=<< 2 , -4, -7 >># Next: # vec(u) + vec(v) = << 5 , -6 , 9>> + << 2 , -4, -7 >># # " " = << (5)+(2) , (-6)+(-4) , (9)+(-7)>># # " " = << 7 , -10 , 2>># The metric norm is therefore: # || vec(u) + vec(v) || = || << 7 , -10 , 2>> || # # " " = sqrt((7)^2 + (-10)^2 + (2)^2 ) # # " " = sqrt( 49 + 100 + 4 ) # # " " = sqrt( 153 ) # # " " = 3sqrt(17) #

Sebastian Acosta · Answer

undefined To find the magnitude of the vector sum <5, -6, 9> + <2, -4, -7>, calculate the sum of the squares of its components and then take the square root of that sum. √((5+2)^2 + (-6-4)^2 + (9-7)^2) = √(7^2 + (-10)^2 + 2^2) = √(49 + 100 + 4) = √153 ≈ 12.37. So, the magnitude of the vector sum is approximately 12.37.

Adrian Ayala · Answer

undefined To find the sum of the two vectors $ \langle 5, -6, 9 \rangle $ and $ \langle 2, -4, -7 \rangle $, you simply add the corresponding components:

$$ \langle 5, -6, 9 \rangle + \langle 2, -4, -7 \rangle = \langle 5+2, -6-4, 9+(-7) \rangle = \langle 7, -10, 2 \rangle $$

To find the magnitude of a vector $ \langle x, y, z \rangle $, you use the formula:

$$ || \langle x, y, z \rangle || = \sqrt{x^2 + y^2 + z^2} $$

So, for the vector $ \langle 7, -10, 2 \rangle $, the magnitude is:

$$ || \langle 7, -10, 2 \rangle || = \sqrt{7^2 + (-10)^2 + 2^2} = \sqrt{49 + 100 + 4} = \sqrt{153} $$

Therefore, $ || \langle 5, -6, 9 \rangle + \langle 2, -4, -7 \rangle || = \sqrt{153} $.

What is # || &lt; 5 , -6 , 9&gt; + &lt; 2 , -4, -7 &gt; || #?

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