Dot Dot Cross
Find the angle between the vectors
veca=<3,-1,5> and vecb=<-2,4,3>
81°
Find the Parametric equations of the line through the points (-8,1,4) and (3,-2,4).
x = -8 + 11t
y = 1 - 3t
z = 4
2veca+3vecb if veca=<1,2,-3> and vecb=<-2,-1,5>
<-4,1,9>
Horizontal: 45.96 ft/sec
Vertical: 38.57 ft/sec
Which of the points (-4,0,-1), (3,1,-5), and (-2,4,6) is closest to the yz-plane?
(-2,4,6)
Find the cross product
veca xx vecb
of the vectors:
veca=<1,3,-2> and vecb=<-1,0,5>
<15,-3,3>
Find the equation of the plane through the point (-1,1/2,3) and with normal vector <1,4,1>.
x + 4y + z = 4
Are the vectors below orthogonal, parallel, or neither?
a) vecu=<-1,2,5>, vecv=<3,4,-1>
b) vecu=<2,6,-4>, vecv=<-3,-9,6>
a) orhogonal
b) parallel
A boat sails south with the help of a wind blowing in the direction S36°E with magnitude 400 lb. Find the work done by the wind as the boat moves 120 ft.
38,832.8 ft-lbs
Find the parametric equations of the tangent line to the curve x = t cos(t), y = t, z = t sin(t) at the point
(-pi,pi,0)
x=-pi-t,
y=pi + t,
z=-pit
Is the line through (-2,4,0) and (1,1,1) perpendicular to the line through (2,3,4) and (3,-1,-8)?
No
Find the equation of the plane through the point (1,-1,-1) and parallel to the plane
5x - y - z = 6
.
5x - y - z = 7
Find the unit tangent vector for the vector function
vecr(t)=<cost,3t,2sin(2t)>
at t = 0.
vecT(0)=<0,3/5,4/5>
Find the length of the curve (correct to 4 decimal places)
vecr(t)=<sint,cost,tant>, 0<=t<=pi/4
1.2780
The equation of the largest sphere with center (5,4,9) that is contained in the first octant.
(x-5)^2+(y-4)^2+(z-9)^2=16
Find the parametric equations of the line through (2,1,0) and perpendicular to both <1,1,0> and <0,1,1>.
x = 2 + t
y = 1 - t
z = t
Find the equation of the plane that contains the line:
x = 1 + t
y = 2 - t
z = 4 - 3t
and is parallel to the plane
5x+ 2y+z=1
5x+2y+z=13
A projectile is fired with an initial speed of 200 m/s and angle of elevation 60 degrees. Find the maximum height reached.
1531 m
Find the equation of the plane that passes through the point (6,0,-2) and contains the line:
x = 4 - 2t
y = 3 + 5t
z = 7 + 4t
33x+10y+4z=190
Three teenagers push a heavy crate across the floor. Dion pushes with a force of 185 N at 0°. Shirley exerts a force of 165 N at 30°, while Joan pushes with 195 N force at 300°. What is the resultant force on the crate?
<425.4, -86.4> N
434.1 N at 348.5°