Adding Vectors by Components Video Lessons

Concept

# Problem: Consider two vectors A and B. expressed in unit vector notation as A = a1i + a2j and B = b1i + b2j.Part (a). Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above.Part (b). Enter an expression for the difference vector A - B in terms of quantities shown in the expressions abovePart (c). Enter an expression for the square of the magnitude of the sum vector | A + B | in terms of quantities shown in the expressions above.

###### FREE Expert Solution

In this problem, we'll perform vector addition and subtraction and determine vector magnitude.

2D vector Magnitude:

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{A}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{A}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{A}}_{\mathbit{y}}}^{\mathbf{2}}}}$

83% (178 ratings)
###### Problem Details

Consider two vectors A and B. expressed in unit vector notation as A = a1i + a2j and B = b1i + b2j.

Part (a). Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above.

Part (b). Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above

Part (c). Enter an expression for the square of the magnitude of the sum vector | A + B | in terms of quantities shown in the expressions above.