3D - 2

Precalc help?

1) IF c=(-3,1) d=(-8,-11) Find c+d c-d 2c+4d 2) Find a non-zero vector perpendicular to the vector represented by (7, -3). Explain how you know they are perpendicular. 3) Find two vectors whose difference is (4, -1, 3). Explain. 4)Find A x B if A=(2,1,3) B=(1,3,0). Verify that the result i perpendicular to A and B. *if you could help me get started on any one of these problems, that'd be awesome. thanks so much brian k!! i actually have a few more questions. maybe you could help me?

Public Comments

1. 1) c+d = (-3+-8,1+-11) = (-11,-10) c-d = (-3--8,1--11) = (-3+8,1+11) = (5,12) 2c + 4d = (2*-3,2*1) + (4*-8,4*-11) = (-6,2)+(-32,-44) = (-38,-42) 2)two vectors are perpendicular if their dot product = 0 (7,-3)dot(x,y)=0 = 7*x + -3*y = 0 = 7x-3y=0 then 7x=3y, which there are many answers to, including: (3,7);(6,14);(-3,-7); etc. 3) vector u = (a,b,c) the vector v = (d,e,f) u - v = (a,b,c) - (d,e,f) = (a - d, b - e, c - f) = (4,-1,3) many answers pick any random number you want so that: a-d=4 ; b-e=-1 ; c-f = 3 such as: (5,5,5) & (1,-6,2) 4) u = (a,b,c) and v = (d,e,f) is u x v = (a,b,c) x (d,e,f) = (bf - ce, cd - af, ae - bd) AxB= (1*0-3*3,3*1-2*0,2*3-1*1) = (-9,3,5) = i Dot product should be zero to verify perpendicular: Adoti = 2*-9 + 1*3 + 3*5 = -18+3+15=0 Good Bdoti = 1*-9 + 3*3 + 0*5 = -9+9+0=0 Good Hope I get them right!