Vector Solutions, Shortcuts, Formulas
Points to Remember
 position vector of a point p(x,y,z) is given as , and it’s magnitude by
 The scalar components of a vector are its direction ratios, and represent its projections along the respective axes.
 The magnitude (r ), direction ratios (a , b, c) and direction cosines (l, m, n) of any vector are related as
 Th e vector sum of the three sides of a triangle taken in order is 0
 The vector sum of two coinitial vectors is given by the diagonal of the parallelogram whose adjacent sides are the given vectors.
 The multiplication of a given vector by a scalar λ , changes the magnitude of the vector by the multiple λ, and keeps the direction same (or makes it opposite) according as the value of λ is positive (or negative).
 For a given a , the vector gives the unit vector in the direction of vector a.
 The position vector of a point R dividing a line segment joining the points P and Q whose position vectors are respectively in the ratio m: nInternally is given by : Externally , is given by :
 The scalar product of two given vector having angle θ between them is define as \vec{a}\cdot Also when is given the angle , θ between the vector may be determine by
 If θ is the angle between two vectors , then their cross product is given as , where unit vector , perpendicular to the plane containing . Such that . form right handed system of coordinate axes.
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