Vectors Flashcards

(6 cards)

1
Q

What is the angle between a line and a plane?

A

Angle Alpha is worked out using the standard form and then doing 90 - theta

π‘Ž. 𝑏 = π‘Ž 𝑏 π‘π‘œπ‘ πœƒ
𝑏. 𝑛 = 𝑏 𝑛 π‘π‘œπ‘ πœƒ
𝑛1. 𝑛2 = 𝑛1 𝑛2 π‘π‘œπ‘ πœƒ

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2
Q

What is the angle between two planes?

A

Angle Alpha is worked out the standard way and then doing 180 - theta

π‘Ž. 𝑏 = π‘Ž 𝑏 π‘π‘œπ‘ πœƒ
𝑏. 𝑛 = 𝑏 𝑛 π‘π‘œπ‘ πœƒ
𝑛1. 𝑛2 = 𝑛1 𝑛2 π‘π‘œπ‘ πœƒ

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3
Q

What is the equation for the shortest distance between a point and a plane?

A

(x, y, z) . (n1, n2, n3) - d / root(n1^2 + n2^2 + n3^3)

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4
Q

What is the equation of a straight line?

A

r = a + Ξ»b

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5
Q

What is the equation of a plane?

A

r = a + Ξ»b + ΞΌc, r.n = d

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6
Q

What is the cartesian equation of a line?

A

πœ† = π‘₯ βˆ’ π‘Ž1 / 𝑏1 = 𝑦 βˆ’ π‘Ž2 / 𝑏2 = 𝑧 βˆ’ π‘Ž3 / 𝑏3

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