Introduction to i and j Vectors

Introduction to i and j Vectors

i and j Vectors

• The unit vectors i and j represent directions along the x and y axes in a 2D space, respectively.

• A vector in 2D space can generally be represented in terms of i and j: Vector V = ai + bj, where a and b are scalar quantities.

Scalar Multiplication and Addition

• Scalar multiplication refers to multiplying a vector by a scalar quantity. The result is a new vector with the same direction but its length scaled by the scalar quantity.

• Vector addition involves adding the corresponding i and j components of the vectors. For example, if Vector A = 3i + 4j and Vector B = i + 2j, then Vector A + Vector B = (3i + i) + (4j + 2j) = 4i + 6j.

Magnitude and Direction

• The magnitude of a vector can be found using Pythagoras’ theorem. For example, the magnitude of the vector V = ai + bj is sqrt(a^2 + b^2).

• The direction of a vector is the angle it makes with the positive x-axis. It’s given by the inverse tan of the ratio of the j component to the i component (tan^-1(b/a)).

Dot Product

• The dot product of two vectors A = a1i + a2j and B = b1i + b2j is a scalar given by A.B = a1b1 + a2b2.