Karteikarten
Vector Basics
Karten in diesem Stapel (13)
- 1Cartesian form means in terms of.....X,Y,Z (e.g. y=2x)
- 2Vector Equation :r = [p1][p2] + λ [d1][d2]
r = [x][y]
[p1][p2] = starting position
λ = parameter (multiple of [d1][d2])
[d1][d2] = direction of line (direction vector) - 3If we have [1][3] + λ [1][2] and we need to find the value of λ to get to [-1/2][0] , we should ....[1][3] + λ[1][2] = [-1/2][0]
Equate top: 1+λ = -1/2 , λ = -3/2
Equate bottom: 3+2λ=0 , λ = -3/2
Both same, therefore λ= -3/2
(if not same then the point doesn't lie on the line) - 4If we change λ, we will get to any place....On the line
- 5Find the vector equation through A[-1][2] and B[5][10]AB = OB - OA ; [5][10] - [-1][2] = [6][8]
r = [1][2] + λ[6][8]
or simplify λ[6][8] to λ[3][4] :
r = [1][2] + λ[3][4] - 6Verify (-1,18) lies on r = [3][2] + λ[-1][4][-1][18] = [3][2] + λ[-1][4]
Equate top (x) : -1=3-λ , λ=4
Equate bottom (y) : 18=2+4λ , λ=4
Therefore point (-1,18) does lie on the line - 7xi + yj is the same as....[x][y]
- 8Find the vector equation of the line through A(2i+j) and B(-3i+3j)AB = OB - OA ; A(2i+j) - B(-3i+3j) = -5i+2j
r= (2i+j) + λ(-5i+2j)
(same as r=[2][1] + λ[-5][2]) - 9Write r=[3][2]+λ[-2][7] in Cartesian from y=mx+cUse point (3,2)
Find gradient using [-2][7] ; -7/2
y-2=-7/2(x-3)
y=-7/2 + 25/2 - 10Vector equation in 3 dimensions:r = [p1][p2][p3] + λ[d1][d2][d3]
- 11Find equation through [1][2][-5] and [-5][6][3]AB = OB - OA : [-5][6][-3] - [1][2][-5] = [-6][4][2] which cancels to [-3][2][1]
So r=[1][2][-5] + λ[-3][2][1] - 12Show 3i-14j+15k lies on r=[1][2][-5] + λ[-3][2][1]3i-14j+15k = -2i+j+5k + λ(i-3j+2k)
Equate i: 3=-2+λ , λ=5
Equate j: -14=1-3λ , λ=5
Equate k: 15=5+2λ , λ=5
Therefore it lies on the line - 13If we get something like 0=0 or 1=1 when finding λ to shoe if a line lies on a line, it means.....That it counts towards it being true, as the statement is true
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- Vector Basics
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- Doc Boff · Jan 2019
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- 29 Jan 2019
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