Vector Algebra

Formulas are organized based on their importance in the CAT exam.
1 Cross Product (Component Form)
2 Parallel Vectors Condition
3 Area of Parallelogram
4 Dot Product of Two Linear Combinations
5 Area of Triangle
6 Condition for Right Angle
7 Triangle Law of Vector Addition
8 Area of Parallelogram
9 Direction Vector of a Line
10 Area of Triangle
11 Vector Component Perpendicular to a Unit Vector
12 Projection of Vector A on B
13 Area of Triangle from Three Points
14 Scalar Triple Product with Linear Combination
15 Dot Product of Different Unit Vectors
16 Scalar Triple Product with Identical Vectors
17 Distance Between Parallel Planes
18 Scalar Triple Product with Repeated Vector
19 Projection of a Vector on Another Vector
20 Collinearity of Three Points
21 Shortest Distance Between Two Skew Lines
22 Collinearity Using Cross Product
23 Right-Hand Rule
24 Volume of Tetrahedron from Four Points
25 Vector Triple Product
26 Scalar Triple Product of Position Vectors
27 External Section Formula
28 Torque for Perpendicular Force
29 Scalar Component Perpendicular to a Vector
30 Magnitude of Difference from Dot Product
31 Lagrange's Identity
32 Lagrange's Identity
33 Scalar and Vector Projections of One Vector onto Another
34 Torque
35 Magnitude of Sum from Dot Product
36 Coplanar Vectors
37 Magnitude of Angular Momentum
38 Dot Product
39 Linear Dependence of Three Vectors
40 Scalar Triple Product
41 Angle Between Two Vectors
42 Perpendicular Vectors
43 Scalar Triple Product
44 Linear Combination of Vectors
45 Section Formula in Vector Form
46 Unit Vector Along a Given Vector
47 Component Perpendicular to a Vector
48 Cross Product of Parallel Vectors
49 Centroid Divides Median
50 Section Point on a Line
51 Dot Product (Component Form)
52 Coplanarity Condition
53 Cross Product Magnitude
54 Dot Product (Geometric Form)
55 Parallel Vectors
56 Coplanarity of Four Points
57 Resultant of Multiple Vectors
58 Vector Along a Given Direction
59 Vector Area of a Triangle
60 Negative of a Vector
61 Point on a Line
62 Collinearity Using Position Vectors
63 Cross Product of Perpendicular Vectors
64 Dot Product and Angle Bisector
65 Vector Triple Product
66 Volume of Parallelepiped from Position Vectors
67 Zero Vector
68 Angular Momentum
69 Vector Area of a Parallelogram
70 Linear Dependence of Two Vectors
71 Cross Product and Perpendicular Direction
72 Distance Between Two Points Using Position Vectors
73 Condition for Intersection of Two Lines
74 Condition for Parallel Vectors Using Components
75 Scalar Triple Product in Determinant Form
76 External Division Ratio
77 Position Vector of Internal Division Point
78 Centroid of a Triangle
79 Representation of a Vector
80 Addition of Vectors
81 Scalar Triple Product and Coplanarity
82 Direction Cosines
83 Cross Product
84 Interchange of Two Vectors
85 Direction Ratios
86 Angle Bisectors of Two Vectors
87 Dot Product of Sum
88 Magnitude of a Vector
89 Vector Components from Direction Cosines
90 Volume of Tetrahedron
91 Unit Vector from Direction Ratios
92 Unit Vector Along the Internal Angle Bisector
93 Coplanarity of Four Points
94 Position Vector
95 Subtraction of Vectors
96 Relation Between Position Vectors
97 Vector Joining Two Points
98 Distance Between Parallel Lines Using Vectors
99 Projection Along a Unit Vector
100 Midpoint Formula in Vector Form
101 Standard Unit Vectors
102 Parallelogram Law of Vector Addition
103 Magnitude of Difference of Two Vectors
104 Area of Parallelogram from Coordinates
105 Scalar and Vector Quantities
106 Direction Cosines from Direction Ratios
107 Angle Between Two Vectors Using Components
108 Direction of Cross Product
109 Vector Triple Product with Parallel Vectors
110 Vector Component Along a Unit Vector
111 Distance from a Point to a Line
112 Internal Division Ratio
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