Determine the scalar product of A= 3.0i + 1.0j - 2.0k and B= 3.0i - 2.0j - 3.0k
Scalar product is the sum of the product of the corresponding components.
For example, the scalar product of
2i+3j+4k and 5i+6j-7k
is
2*5+3*6-4*7=10+18-28=0
CNS
To determine the scalar product (also known as the dot product) of two vectors A and B, you need to multiply their corresponding components and then sum the results.
Given vectors A and B:
A = 3.0i + 1.0j - 2.0k
B = 3.0i - 2.0j - 3.0k
The scalar product (A · B) is calculated as follows:
A · B = (3.0 * 3.0) + (1.0 * -2.0) + (-2.0 * -3.0)
Simplifying the calculations, we have:
A · B = 9.0 - 2.0 + 6.0
Combining like terms:
A · B = 13.0
Therefore, the scalar product of A and B is 13.0.
To determine the scalar product, also known as the dot product, of two vectors A and B, you need to multiply the corresponding components of the two vectors and then sum up the results. The formula for the dot product is as follows:
A · B = (Ax * Bx) + (Ay * By) + (Az * Bz)
Let's break it down step by step for the given vectors A and B:
A = 3.0i + 1.0j - 2.0k
B = 3.0i - 2.0j - 3.0k
Ax = 3.0
Ay = 1.0
Az = -2.0
Bx = 3.0
By = -2.0
Bz = -3.0
Now, substitute the values into the formula:
A · B = (3.0 * 3.0) + (1.0 * -2.0) + (-2.0 * -3.0)
A · B = 9.0 - 2.0 + 6.0
A · B = 13.0
Therefore, the scalar product of A and B is 13.0.