Why vectors cannot be added algebraically?

Question

6678 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-05-16T00:50:01

You actually can add vectors algebraically, but they need to be in unit vector notation first.

If you have two vectors #vec(v_1)# and #vec(v_2)#, you can find their sum #vec(v_3)# by adding their components.

#vec(v_1) = ahat ı + bhat ȷ#
#vec(v_2) = chat ı + dhat ȷ#
#vec(v_3) = vec(v_1) + vec(v_2) = (a + c)hat ı + (b+d)hat ȷ#

If you wish to add two vectors, but you only know their magnitudes and directions, first convert them to unit vector notation:

#vec(v_1) = m_(1)cos(theta_1)hat ı + m_(1)sin(theta_1)hat ȷ#
#vec(v_2) = m_(2)cos(theta_2)hat ı + m_(2)sin(theta_2)hat ȷ#

Then find their sum normally:

#vec(v_3) = vec(v_1) + vec(v_2)#
#vec(v_3) = (m_(1)cos(theta_1) + m_(2)cos(theta_2))hat ı + (m_(1)sin(theta_1) + m_(2)sin(theta_2))hat ȷ#