FP3 Vectors Flashcards

(15 cards)

1
Q

Distance of point to line equation

(Point: c, Line: a + λb)

A

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2
Q

Distance between parallel lines equation

(Points on lines: a1/a2, Direction Vector: b)

A
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3
Q

Distance between skew lines equation

(Points on lines: a1/a2, Direction Vectors: b1/b2)

A
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4
Q

How to work out the angle between two planes

A

Use scalar product to find the angle between the normals (therefore a= n1, b=n2)

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5
Q

How to work out the angle between a line and a plane

A

Use the scalar product to find the angle between the line’s direction and the plane’s normal, and subtract this value from 90°

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6
Q

How to work out line of intersection of 2 planes

A

The direction vector of the line of intersection is perpendicular to both plane’s normals, therefore:

n1 x n2 = b

Then use simputaneous equations to find a point on both planes and this will be a, for line equation in form:

r = a + λb

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7
Q

Distance of point to plane

(Plane equation in form: r.n=d where n is the normal, r is a general point. Position of point: a)

A

Use equation: Distance=

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8
Q

Area of triange

A
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9
Q

Area of Parallelogram

A
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10
Q

Volume of Parallelepiped

A

Where a and b represent vector sides of the parallelogram at the base and c represets the vector upwards in the 3rd dimension:

Note: a.(bxc) = b.(cxa)

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11
Q

Volume of Tetrahedron

A

Same term definitions as volume of parallelepiped

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12
Q

Vector cross product formula

A

Where n stands for a unit vector perpendicular to both a and b. (in the direction that a right handed screw would move when turned a -> b)

Note: b x a = -a x b, and to find a unit vector, divide the vector by it’s magnitude.

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13
Q

What is an alternate equation for a straight line in vector form?

A

(r-a) x b= 0

Can also be written as rxa - axb = 0 and hence as

rxa=axb)

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14
Q

What are the different forms for the eqaution of a plane?

A

r.n=a.n (r.n=d)

(which can be converted to catesian form by inputting r= xi+yj+zk)

r= a + λb + μc

Where a is the position vector of a point in the plane, b and c are non-parallel vectors in the plane and r in the position vector a general point on the plane.

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15
Q

How to find the point of intersection of a line and a plane.

A

Enter the line in column matrix form and substitute for r in the plane’s eqation, r.n=a.n .

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