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16 Cards in this Set

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 What is the right hand rule? If thumb is z axis, if you close your open palm it goes from the x to the y axis. What is the distance formula in 3 dimentions? D = Sqrt[(x{2} - x{1})^2 + (y{2} - y{1})^2 + (z{2} - z{1})^2] What is the midpoint of two other points in three dimentions? Midpoint = ( ((x{1}+x{2})/2), ((y{1}+y{2})/2), ((z{1}+z{2})/2) ) What is the equation of a sphere in R^3 with center at (h, k, j) and radius r ? (x-h)^2 + (y-k)^2 + (z-j)^2 = r^2 What is a vector? A vector is a quantity that has both magnitude and direction. What is the zero vector? A vector whose lenghth is zero that points in any (and all) directions. How do you do vector addition and subtraction? Vector addition and subtraction are done by simply doing piecewise addition and subtraction of each of the vectors components two parts. How do you calculate a scalar times a vector? A scalar times a vector results in the same vector with each component of the vector multiplied by the scalar. What is a scalar? A scalar is not a vector. A scalar is simply a number like 4 or a variable like z. What is the vector projection of vector b onto vector a? proj(a)b How do you calculate the dot product of two vectors? given vector A and vector B: A.B = a{1}*b{1} + a{2}*b{2} + a{3}*b{3} List the properties of dot products Given vector a, vector b, and vector c: a.a = |a|^2 a.(b+c)=a.b+a.c a.b=b.a (given k scalar)k(a.b)=(ka).b=a.(kb) a.(the zero vector) = (the number 0, not the vector 0, but the number 0) What is the geometric interpretation of the dot product? Given vector a and vector b: a.b = |a|*|b|*cos(theta) What is the scalar projection of vector A onto vector B? Fill in later What is the Cross Product? The Cross Product of vector A and B is the resultant vector perpendicular to the plane formed by A and B in the direction of the right hand rule. AXB = List the properties of cross products? Given vector A, vector B, and vector C: 1)A X B = -(B X A) 2)A X A = 0 3)The vector A X B is orthogonal to both a and B. -If vector v = A X B, then v.A = 0 & v.B = 0 4)A X (B+C) = A X B + A X C 5)A.(B X C) = scalar triple product = (a X B).C 6)A X (B X C) = vector triple product = (A.C)b-(a.b)C