If A = and B = then find |A-B| and 2A + 3B. If A = i + 2j + k and B = 2i + 2j -
ID: 3017623 • Letter: I
Question
If A = and B = then find |A-B| and 2A + 3B. If A = i + 2j + k and B = 2i + 2j - 3k, then find A times B and verify that it is orthogonal to A by using the dot product. For the triangle given by vertices A = (3, 1, -1), B = (1, 0, 4) and C = (2, 3, 4) what is the angle at vertex A. What is the area of the triangle? Give the vector equation for the line which goes through (-1, 4, 2) and (1, 1, 5). Where does it pass through the z = 0 plane? Give the equation for the plane which goes through the origin, (2, 0, -1) and (1, -1, 3). Find the unit tangent vector to the curve r vector (t) = ti - sin(2t) j - cos(2t) k when t = 0. Find the arc length of the parametric curve from t = 0 to t = 1. Find the curvature for y = x^2 when x = - squareroot 2 using the formula K = |f"(x)|/[1 + (f'(x))^2]^3/2 Find T vector (t),T vector (pi /2), N vector (pi /2) for the vector equation r vector (t) = ti - sin(t)j + cos(t) k The acceleration of a particle is a(t) = the initial velocity is and the original position is Find the equation for the position vector.Explanation / Answer
A = <0,1,3>
B = <-2,0,4>
|A - B|
A - B = <0,1,3> - <-2,0,4> which is <2,1,-1>
So, |A-B| = sqrt(2^2 + 1^2 + (-1)^2)
= sqrt(6)
2A + 3B :
2<0,1,3> + 3<-2,0,4>
<0,2,6> + <-6,0,12>
which becomes
<-6,2,18>