Find the quantity if v = 5i - 7j and w = 3i + 2j.
-$\| \mathrm { v } + \mathrm { w } \|$
A) $2 \sqrt { 6 } + \sqrt { 13 }$
B) $\sqrt { 74 } + \sqrt { 13 }$
C) $\sqrt { 39 }$
D) $\sqrt { 89 }$

Question

Quizplus · Accepted Answer

To find the magnitude of $ \mathbf{v} + \mathbf{w} $, first add the vectors: $ \mathbf{v} + \mathbf{w} = (5\mathbf{i} - 7\mathbf{j}) + (3\mathbf{i} + 2\mathbf{j}) = 8\mathbf{i} - 5\mathbf{j} $. Then, calculate the magnitude: $ \| \mathbf{v} + \mathbf{w} \| = \sqrt{(8)^2 + (-5)^2} = \sqrt{64 + 25} = \sqrt{89} $.

Find the Quantity If V = 5i - 7j and W