Consider the two vectors Aarrowbold = 3 i hat bold − 3 j hat bold and Barrowbold = − i hat bold − 6 j hat bold.
To consider the two vectors A → = 3 i ^ - 3 j ^ and B → = - i ^ - 6 j ^ , we can perform various operations and calculations. Let's go step by step:
1. Vector Addition:
To add two vectors, simply add their corresponding components.
So, A → + B → = (3 i ^ - 3 j ^) + (-i ^ - 6 j ^)
= (3 - 1) i ^ + (-3 - 6) j ^
= 2i ^ - 9j ^
Therefore, the resultant vector obtained by adding A → and B → is R → = 2i ^ - 9j ^ .
2. Scalar Multiplication:
To multiply a vector by a scalar, multiply each component of the vector by that scalar.
For example, if we multiply A → by 4, the result will be:
4A → = 4(3 i ^ - 3 j ^)
= 12 i ^ - 12 j ^
So, the result of scalar multiplication is 12 i ^ - 12 j ^ for the vector A →.
3. Dot Product:
The dot product of two vectors A → and B → is given by the formula:
A → · B → = A x B x + A y B y
= (3)(-1) + (-3)(-6)
= -3 + 18
= 15
Therefore, the dot product of A → and B → is 15.
These are the basic operations that can be performed with the given vectors A → and B →.