Linear Algebra. Solving Equations

Question

Let →a=<−2,−3,4>a→=<-2,-3,4> and →b=<−2,5,1>. Find →a + 2b

Answer 1

<-2,-3,4> + <-2,5,1> = <-2-2, -3+5, 4+1> =<-4,2,5>

same as adding vectors in 2 dimensions

3 dimensions is a little harder to visualize, 4 dimensions impossible

<c,d> + <e,f> = <c+e,d+f>

such as for example:

<1,2>+<2,1> = <3,3>

add them like you would the x and y coordinates of two points

graph the points, construct a parallelogram with sides from the origin to one point and from the origin to the other point. construct 2 more parallel sides. find the 4th vertex of the parallelgram, <3,3>

the magnitude of the resultant vector is found using the pythagorean theorem d^2=3^2+3^2, d=3sqr2

the direction is the angle = 45 degrees = tan^-1(change in y/change in x) =tan-1(3/3) = the angle whose tangent = 1 which is pi/4 = 45 degrees which gives you the polar coordinates of the constructed parallelogram's 4th vertex