Test 1 Flashcards
(34 cards)
Two vectors are parallel in the same direction if a^=
c*b^ and c>0
Unit vector =
direction/magnitude
Find a vector length 2 in the same direction as 3i^-4j^
2(unit vector for 3i^-4j^)
How to take dot product
multiply corresponding components and then sum all together
Dot product results in a…
scalar quantity
The dot product helps find…
the angle between 2 vectors
What equation helps find the angle between 2 vectors?
cos(theta) = (a^ dot b^)/(mag(a)*mag(b))
a^ and b^ are perpendicular if
dot product is 0
How to prove <2,4> and <6,-3> are orthogonal
Take dot product. It would equal 0.
Statics use for cross product
M = r^ x F^
det |ab/cd| =
ad-bc
How to take cross product
i^ j^ k^ / a1^ a2^ a3^ / b1^ b2^ b3^ |
cofactor expansion
i^det-j^det+k^det
sign for i,j,k
(-1)^row+column
a^ x b^ is ______________ to the plane formed by vectors a^ and b^
perpendicular
if a^ x b^ = 0, then
a^ is parallel to b^
length of cross product can be calculated by
finding the area of the parallelogram formed by a^ and b^, which is || a^ x b^ ||
1/2 || a^ x b^ || =
area of triangle formed by a^ and b^
What do you need to plot a line in 3D?
Point (x1, y1, z1) and parallel vector (slope)
What parametric equations are used to plot a line?
x = x1 + a1t y = y1 + a2t z = z1 + a3t Point (x1, y1, z1) Parallel vector
How do you plot a line given two points?
P2-P1 gives parallel vector. Use P1 as point.
What do you need to plot a plane in 3D?
1) point from shared tail
2) perpendicular vector found from cross product
Given three points. Steps to find equation of plane:
1) Subtract points to find vectors
2) Take cross product of vectors (gives perpendicular vector) (n^=<i>)
3) plugs values of equation using n vector and point from shared tail
n1(x-x1)+n2(x-x2)+n3(x-x3)=0</i>
plane point normal form
-18(x-3)+0(y-2)+24(z-1)=0
plane standard form
-18x+24z+30=0
