Addition of Vectors: Addition of vectors involves combining two or more vectors into a single new vector. The resultant vector has the same direction and ma...
Addition of Vectors:
Addition of vectors involves combining two or more vectors into a single new vector. The resultant vector has the same direction and magnitude as the original vectors, but it has a different starting position.
To add two vectors, we simply add their corresponding component values. For example, if vectors A and B have components A_1 and A_2, and vectors C and D have components C_1 and C_2, then A + B = (A_1 + C_1, A_2 + C_2).
Scalar Multiplication:
Scalar multiplication is a special case of scalar multiplication that involves multiplying a vector by a scalar (a single number). The scalar multiplies each component of the vector by the corresponding component value, and then adds the results together.
For example, if vector A has components A_1 and A_2, and scalar k is 2, then k * A = (2 * A_1, 2 * A_2).
Examples:
Let's consider the following two vectors:
A = (2, 4, 6)
B = (3, 6, 9)
Then, A + B = (5, 10, 15)
And, 3 * A = (6, 12, 18)