Vector Algebra

Formulas are organized based on their importance in the CAT exam.
1 Vector Area of a Triangle
2 Collinearity Using Cross Product
3 Condition for Right Angle
4 Magnitude of Difference of Two Vectors
5 Parallel Vectors Condition
6 Vector Component Along a Unit Vector
7 Area of Triangle
8 Cross Product (Component Form)
9 Triangle Law of Vector Addition
10 Internal Division Ratio
11 Area of Parallelogram
12 Area of Parallelogram
13 Scalar Triple Product with Linear Combination
14 Direction Vector of a Line
15 Dot Product of Two Linear Combinations
16 Area of Triangle
17 Vector Component Perpendicular to a Unit Vector
18 Projection of Vector A on B
19 Area of Triangle from Three Points
20 Dot Product of Different Unit Vectors
21 Scalar Triple Product with Identical Vectors
22 Scalar Triple Product with Repeated Vector
23 Distance Between Parallel Planes
24 Projection of a Vector on Another Vector
25 Collinearity of Three Points
26 Shortest Distance Between Two Skew Lines
27 Volume of Tetrahedron from Four Points
28 Vector Triple Product
29 Scalar Triple Product of Position Vectors
30 External Section Formula
31 Torque for Perpendicular Force
32 Scalar Component Perpendicular to a Vector
33 Magnitude of Difference from Dot Product
34 Lagrange's Identity
35 Lagrange's Identity
36 Torque
37 Scalar and Vector Projections of One Vector onto Another
38 Magnitude of Sum from Dot Product
39 Right-Hand Rule
40 Dot Product
41 Coplanar Vectors
42 Magnitude of Angular Momentum
43 Linear Dependence of Three Vectors
44 Scalar Triple Product
45 Angle Between Two Vectors
46 Perpendicular Vectors
47 Scalar Triple Product
48 Section Formula in Vector Form
49 Unit Vector Along a Given Vector
50 Component Perpendicular to a Vector
51 Cross Product of Parallel Vectors
52 Centroid Divides Median
53 Section Point on a Line
54 Linear Combination of Vectors
55 Coplanarity Condition
56 Cross Product Magnitude
57 Dot Product (Geometric Form)
58 Parallel Vectors
59 Resultant of Multiple Vectors
60 Dot Product (Component Form)
61 Coplanarity of Four Points
62 Negative of a Vector
63 Vector Along a Given Direction
64 Point on a Line
65 Collinearity Using Position Vectors
66 Cross Product of Perpendicular Vectors
67 Dot Product and Angle Bisector
68 Vector Triple Product
69 Volume of Parallelepiped from Position Vectors
70 Angular Momentum
71 Vector Area of a Parallelogram
72 Linear Dependence of Two Vectors
73 Cross Product and Perpendicular Direction
74 Zero Vector
75 Distance Between Two Points Using Position Vectors
76 Condition for Intersection of Two Lines
77 Condition for Parallel Vectors Using Components
78 Scalar Triple Product in Determinant Form
79 External Division Ratio
80 Position Vector of Internal Division Point
81 Centroid of a Triangle
82 Representation of a Vector
83 Addition of Vectors
84 Scalar Triple Product and Coplanarity
85 Direction Cosines
86 Cross Product
87 Interchange of Two Vectors
88 Direction Ratios
89 Angle Bisectors of Two Vectors
90 Dot Product of Sum
91 Magnitude of a Vector
92 Vector Components from Direction Cosines
93 Volume of Tetrahedron
94 Unit Vector from Direction Ratios
95 Unit Vector Along the Internal Angle Bisector
96 Coplanarity of Four Points
97 Position Vector
98 Subtraction of Vectors
99 Relation Between Position Vectors
100 Vector Joining Two Points
101 Distance Between Parallel Lines Using Vectors
102 Projection Along a Unit Vector
103 Parallelogram Law of Vector Addition
104 Scalar and Vector Quantities
105 Direction Cosines from Direction Ratios
106 Angle Between Two Vectors Using Components
107 Area of Parallelogram from Coordinates
108 Direction of Cross Product
109 Vector Triple Product with Parallel Vectors
110 Midpoint Formula in Vector Form
111 Standard Unit Vectors
112 Distance from a Point to a Line
113 Centroid in Cartesian Coordinates
114 Point Dividing a Line Segment in a Given Ratio
115 Vector Equation of a Line
116 Coplanarity of Two Lines
117 Foot of Perpendicular from a Point to a Plane
118 Angle Between Two Lines
119 Parallel Planes
120 Magnitude of Sum of Two Equal Vectors
121 Plane Through Three Points
122 Square of Difference of Two Vectors
123 Angle Between a Vector and a Coordinate Axis
124 Vector Triple Product Formula
125 Cross Product in Component Form
126 Vector Triple Product Is Not Associative
127 Perpendicular Lines
128 Magnitude of a Vector
129 Line Through Two Points
130 Plane Through a Point
131 Magnitude in Component Form
132 Scalar Multiplication
133 Vector Projection
134 Vector Identity for Difference of Squares
135 Distance Between Two Points in Cartesian Form
136 Unit Vector
137 Reflection of a Point in a Plane
138 Magnitude of Torque
139 Cross Product with Itself
140 Angle Between Two Planes
141 Magnitude of a Cross Product Squared
142 Resolution Along Coordinate Axes
143 Coplanarity Using Determinant
144 Alternative Vector Triple Product
145 Equilibrium of Vectors
146 Vector in Component Form
147 Angle for Parallel Vectors
148 Projection Magnitude
149 Magnitude of Difference of Two Equal Vectors
150 Area of Triangle from Coordinates
151 Midpoint Through Position Vectors
152 Direction Cosine Relation
153 Resultant of Parallel Vectors
154 Dot Product of Difference
155 Volume of Parallelepiped
156 Work Done by a Constant Force
157 Minimum Resultant
158 Maximum Resultant
159 Line Perpendicular to a Plane
160 Resolution of a Vector
161 Resultant Range
162 Dot Product in Component Form
163 Resultant of Two Perpendicular Vectors
164 Distance Between Parallel Lines
165 Triangle Inequality
166 Square of Sum of Two Vectors
167 Dot Product from Sum and Difference
168 Position Vector of Centroid Using Median
169 Distance of a Point from a Plane
170 Cross Product of Two Linear Combinations
171 Condition for Parallel Vectors Using Cross Product
172 Magnitude Under Scalar Multiplication
173 Angle Between a Line and a Plane
174 Condition for Acute Angle
175 Scalar Triple Product and Determinant Sign
176 Cyclic Property of Scalar Triple Product
177 Dot Product of Unit Vectors
178 Resultant of Opposite Vectors
179 Distance Between a Point and a Line
180 Determinant Form of Cross Product
181 Scalar Triple Product as Dot Product
182 Magnitude Using Dot Product
183 Scalar Multiplication in Dot Product
184 Unit Vector
185 Scalar Multiplication in Cross Product
186 Parallelogram Identity
187 Parallel Lines
188 Reverse Order in Cross Product
189 Cross Product of a Vector with a Vector Triple Product
190 Magnitude of Cross Product
191 Self Dot Product
192 Distributive Property of Cross Product
193 Condition for Obtuse Angle
194 Equal Vectors
195 Projection and Dot Product Relation
196 Position Vector of a Point
197 Resultant Direction
198 Scalar Projection Using Dot Product
199 Normal Vector to a Plane
200 Perpendicular Planes
201 Plane Through Origin
202 Cross Product of Unit Vectors
203 Line Parallel to a Plane
204 Volume of Tetrahedron from Coordinates
205 Unit Vector Along the External Angle Bisector