Work
OR
|F||AB|cos(theta)
Formulas for the distance from:
1. point S to vector V with point T on V
2. point S(x_0,y_0) to cartesian line Ax+By+C=0
1. proj (ST/V_p)
2. |Ax_0+By_o+C|/sqrt(A^2+B^2)
with the point (-8,6) on L1
L1: <-8,6>+t<-5,3>
Formula to find the projection of vector a onto vector b
proj(a/b) = (a*b)/|b|
What is a vector??
something with a length and direction
It takes 50 foot-pounds of work to move a box along the horizontal ground. Give one possible weight of the box and distance it moved
one ex: 50 pound box, moved 1 foot
Find the distance from point P (-2,3) to the line given by L:<-1,2>+t<3,4>
7/5
Find the parametric vector equation of the line
y=2x +1
L: <0,1>+t<1,2>
For what angle theta between vectors a and b is the projection of a onto b = |a|sqrt(3)/2
30 degrees
What is a scalar??????????
just length
A 1 pound box is being pulled along a ramp inclined at 3.4568 degrees. The pulling force is parallel to the inclined plane. Find the work done to move the box 7000 feet along the ramp
7000 foot-pounds
Find the distance from the point (3,2) to the line
y = 8/3x-11
15/sqrt(73)
Find the intersection of the following parametric equations:
L1: <-3,4>+t<5,6>
L2: <2,0>+t<5,1>
(-8,-2)
When is the projection of vector a onto b exactly equal to the dot product of a and b?
when b is a unit vector
TIMED QUESTION: MAX TIME - 1.5 MINUTES
Find the orthocenter (point of concurrency for the 3 altitudes) for the following triangle where m is any real positive number:
A(0,m) B(m,0) C(0,0)
(0,0)
A 10 pound box is now being pulled up a ramp inclined at 11 degrees. The box is being pulled at an angle of 12 degrees to the horizontal. What force must we pull at so that the effective force is exactly 13 pounds? (EXACT VALUE)
13/cos(1)
Find the distance between the lines given by:
y - 8 = -2(x+1) and
L: <4,7>+t<-2,4>
9/sqrt(5)
Find the circumcenter of triangle ABC where A=(0,1) B = (2,0) anc C= (4,4). Note: the circumcenter is the point 2/3 way from the vertex to the midpoint of the opposite side.
X = mdpt CB = (3,2) so AX = <3,1> so 2/3AX = <2,2/3>. Circumcenter P = (0,1) + (2,2/3) = (2,5/3)
DAILY DOUBLE:
let a = 3n + 3sqrt(3)n_p
Find scalar proj (3n/a)
1.5|n|
A circle of radius 5sqrt(17) has is tangent to the line L: <-1,3>+t<1,4> at the point (0,7). Find the center of the circle
(-20,12) or (20,2)
A box is being pulled at a force of 15 pounds in the direction <2,1> a distance of 2 feet along the line
y=(2/3)x. Find the work done (EXACT VALUE)
240/sqrt(65)
or : 48(sqrt65)/13
TIMED QUESTION: 1.5 MINUTE MAX
Given that a and b are any real numbers, find the distance between the lines:
L: <a,8> + t<-13,801>
13x+801y+8=0
0, the lines intersect
L1 : <-3,4> + t<6,8>
L2 parallel to L1. Find the equation(s) of L2
L2: <-3-8r, 4+6r> + t<6,8>
L2: <-3+8r, 4-6r> +t<6,8>
Let vector v = <a, 0> where a is any positive real number. Let vector w be a length of a in the direction of the line y = b/a x + c where a,b, and c form a Pythagorean triple (a^2+b^2 = c^2). Find the scalar proj of w onto v only in terms of b and c
a^2/c = c-b^2/c
Find the orthocenter (point of concurrency for the 3 altitudes) for the following triangle:
A(0,1) B(4,2) C(2,6)
parametric equation:
<0,1>+t<4,2>=<4,2>+t<-5,2>
intersection: (26/9, 22/9)