This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 251 Section 3: Review for Test2
Test2 covers Section10.1 through Section 10.7 (except for 10.6) in calculus. Here is the highlight of each section. Section10.1 The distance between two points; the equation of a sphere. Section10.2 Vector addition, subtraction and scalar multiplication (by geometric as well as algebraic methods); the length of a vector; unit vector. Section10.3 The denition of a · b; the angle between two vectors; projection of a vector onto another vector. Section10.4 The denition of a × b; the direction of a × b ; the length of a × b and the geometric interpretation of a × b. Section10.5 The vector equation, parametric equations and symmetric equations of a line; the normal vector of a plane; the equation of a plane; the angle between two planes. Section10.7 Vector equations of space curves; derivatives and tangent vectors; nd the tangent line to a space curve. Here is the list of facts and formulas that you need to memorize. 1. The distance between two points is given by
P1 P2  = (x2 − x1 )2 + (y2 − y1 )2 + (z2 − z1 )2 . 2. The equation of a sphere with center (x0 , y0 , z0 ) and radius r is given by
(x − x0 )2 + (y − y0 )2 + (z − z0 )2 = r2 . 3. a · b = a1 b1 + a2 b2 + a3 b3 = ab cos θ .
1 ijk 4. a × b = a1 a2 a3 b1 b 2 b3 and a × b = ab sin θ. (The following facts should be understood instead of just memorized.) 5. The vector equation of a line through P0 (x0 , y0 , z0 ) and parallel to the vector v = a, b, c is given by r = r0 + tv or
x, y, z = x0 , y0 , z0 + t a, b, c . 6. The equation of the plane passing through P0 (x0 , y0 , z0 ) with normal vector v = a, b, c is
a(x − x0 ) + b(y − y0 ) + c(z − z0 ) = 0. 7. The tangent vector of a given the space curve r(t) = x(t), y (t), z (t) is
r (t) = x (t), y (t), z (t) . 2 ...
View Full
Document
 Spring '09
 CGHEN
 Calculus, Addition

Click to edit the document details