Physics Help Forum Combining like terms?

 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum

 Sep 27th 2009, 12:52 PM #1 Junior Member   Join Date: Sep 2009 Posts: 1 Combining like terms? This may come across as a rather silly question, but I'm having troubles combining like terms for a problem in physics (first year university level). Please note: ie. A(rightarrow) means a vector of A (A with the right arrow overtop) ie. i(hat) is a unit vector i (with the hat overtop it) ie. j(hat) is a unit vector j (with the hat overtop it) The question: 1. Write each vector in terms of the unit vectors i(hat) and j(hat). Use the unit vectors to express the vector C(rightarrow) where C(rightarrow) = 3.00A(rightarrow) - 4.00B(rightarrow). Find the magnitude and direction of C(rightarrow). My work so far: 2. Relevant equations A(rightarrow) = Axi(hat) + Ayj(hat) Ax = 3.60cos(70deg.)=1.23 Ay = 3.60sin(70deg.)=3.38 A(rightarrow) = 1.23i(hat) + 3.38j(hat) B(rightarrow) = Bxi(hat) + Byj(hat) Bx = -2.4cos(30deg.)=-2.078 By = -2.4sin(30deg.)=-1.2 B(rightarrow) = -2.078i(hat) + (-1.2)j(hat) 3. The attempt at a solution C(rightarrow) = 3.00A(rightarrow) - 4.00B(rightarrow) C(rightarrow) = 3.00(1.23i(hat) + 3.38j(hat)) - 4.00(-2.0781i(hat) + (-1.2)j(hat)) C(rightarrow) = (3.69i(hat) + 10.14j(hat)) - (-8.312i(hat) + (-4.8)j(hat)) I got stuck at this stage; I'm pretty sure up until now I've been doing it right, but now I'm a little confused about combining the like terms (ie. ihat with ihat and jhat with jhat terms). Would I, for instance with the jhat terms, go 10.14-(-4.8) which would give me a large positive number? or would I just go 10.14(-4.8) which equals 5.34, and then subtract it later (ie. -4.622i(hat) - 5.34j(hat))? Basically, I just need to know what to do from here. I'm pretty sure I know how to solve for the magnitude and direction once I figure out these terms. Note: A similar, simpler question to this one would be how to combine the like terms for this one: A(rightarrow) - B(rightarrow) (4.00i(hat) + 3.00j(hat)) - (5.00i(hat)+(-2.00)j(hat)) Would the answer for that one be 9.00i(hat) - 1.00j(hat)? I know it's simple algebra but for some reason it's evading me =\ Thanks for any help! Last edited by dark-ryder341; Sep 27th 2009 at 12:55 PM.
 Sep 29th 2009, 04:36 AM #2 Physics Team   Join Date: Feb 2009 Posts: 1,425 One request please. Could you rewrite this using boldface i j k for the unit vectors and A etc. for vectors? Hats off to you for writing it like this, but im kind of getting lost in them, so get the hats off the unit vectors!

 Tags combining, terms

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post noabsortion1 Light and Optics 0 Apr 28th 2016 08:33 PM timemachine2 Light and Optics 6 Feb 5th 2016 07:54 PM Robot_Maker20 Advanced Thermodynamics 0 Oct 1st 2010 12:48 PM synclastica_86 Light and Optics 1 Nov 8th 2009 10:02 PM taichi2910 Advanced Electricity and Magnetism 1 May 19th 2009 04:17 AM