Скачать или смотреть ADDITION,SUBTRACTION AND MULTIPLICATION OF A VECTORI 2-D I CBSE, CHSE I MTH I N S SIR l

Vector addition and subtraction are performed by adding or subtracting the corresponding components, resulting in a new vector. Subtraction can be visualized as adding a negative vector, which reverses the direction of the subtracted vector. For scalar multiplication, a vector is multiplied by a single number (scalar), changing its magnitude and potentially reversing its direction if the scalar is negative, while keeping the direction the same if positive.

*Graphical (Head-to-Tail) Method*:

*Addition*: Place the tail of the second vector at the head (tip) of the first vector. The resultant vector (the sum) is drawn from the tail of the first vector to the head of the second.
*Subtraction*: To subtract vector B from vector A (A - B), you can change the direction of vector B (making it -B) and then add it to A using the head-to-tail method.

*Scalar Multiplication
Component-wise multiplication*: Multiply each component of the vector by the scalar (a single number).
If v = (x, y) and k is a scalar, then k * v = (k * x, k * y).
*Effect on the vector*:
If the scalar is positive, the resulting vector has a new magnitude but points in the same direction.
If the scalar is negative, the resulting vector has a new magnitude and points in the opposite direction.