Home >> PURE MATHS, Vectors, vector equations

Component Rules

Consider two vectors in three dimensional space.

Where 'm' is a scalar quantity.

Hence, the magnitudes of a and b are given by:

In 3D space, if point A has position vector a and point B has position vector b then the distance AB is given by:

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Equation of a Straight Line - single point & parallel vector given

A(x₁ y₁ z₁) is a fixed point on the line.

a is the position vector for point A   a = x₁i + y₁ j+ z₁k

s is a vector parallel to the line   s = l i + m j+ n k

(l m n are called the direction ratios of the line)

r is the position vector for an arbitrary point P(x, y, z) on the line.

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Equation of a Straight Line - two points given

A(x₁ y₁ z₁) is a fixed point on the line

a is the position vector for point A   a = x₁i + y₁ j+ z₁k

B(x₂ y₂ z₂) is a fixed point on the line

b is the position vector for point B   b = x₂i + y₂ j+ z₂k

r is the position vector for an arbitrary point P(x, y, z) on the line.

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