Vector Equation of a Straight Line & Three Dimensional Co-ordinate Geometry problem

May 29th, 2015
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Example : Let A=(8-7,0) and B=(2,-1, -3) (a) Find the equation of the straight line . (b) Find the perpendicular distance from the point to the line . Find also the foot of perpendicular.

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vectorsDefinition of VectorA vector is a quantity with a magnitude and a direction, represented by an arrow.A vector has head A and tail B, represented as , or as a lowercase letter ,.Do not think of vector has a segment with a fixed place. It is actually embedded throughout the coordinate plane.2 vectors are equal if their magnitudes and directions are equal.A zero vector has no magnitude; it starts and ends at A.Adding and Subtracting VectorsGiven 2 vectors, and , draw and . Vector is called the sum of vectors and . Paralellogram ruleIf ABCD is a parallelogram, then .Properties of Vector AdditionIf are vectors, then: (Commutative Property)( (Associative Property) (Identity Property of Addition) Difference of 2 Vectors is the vector with the same magnitude but opposite direction with .Given 2 vectors and , the difference of and is vector , notated as .Given 3 points A, B, C, we have .Multiplying a Vector with a ScalarGiven real number k ? 0 and vector ? 0. The product of k and is notated and has the same direction with if k > 0 and has the opposite direction with if k < 0, and has magnitude We define 0.Properties of Multiplying a Vector with a

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