Concept

# Problem: The sum of two vectors is the largest when the two vectors are _____.A. pointing in the same directionB.pointing in the same direction C. pointing in opposite directionsD. perpendicular to each otherE. positioned at a 45

###### FREE Expert Solution

The magnitude of the sum of two vectors is expressed as:

$\overline{){\mathbf{|}}{\mathbf{A}}{\mathbf{+}}{\mathbf{B}}{\mathbf{|}}{\mathbf{=}}\sqrt{{\mathbf{A}}^{\mathbf{2}}\mathbf{+}{\mathbf{B}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{A}\mathbf{B}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}}$

Assessing the options given, we know that the magnitude of vectors A and B are fixed.

Therefore, the magnitude of the sum of these vectors depends only on the angle, θ between them.

If the vectors are in the same direction, θ = 0°

Thus, |A + B| = sqrt [A2 + B2 + 2AB cos(0°)] = sqrt(A2+B2+2AB) = A + B

When the two vectors are pointing in the opposite direction, θ = 180°

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###### Problem Details
The sum of two vectors is the largest when the two vectors are _____.

A. pointing in the same direction
B.pointing in the same direction
C. pointing in opposite directions
D. perpendicular to each other
E. positioned at a 45