Find the scalar product a.b. If a = 2i + 3j + 4k and b = 5i - 2j + k
2*5 + 3*-2 + 4*1
10 - 6 + 4
8
Does vector products and vector geometry have relievance
To find the scalar product of two vectors, a and b, you need to take the dot product of the two vectors.
Given that a = 2i + 3j + 4k and b = 5i - 2j + k, the dot product can be calculated as follows:
a.b = (2 * 5) + (3 * -2) + (4 * 1)
= 10 - 6 + 4
= 8
Therefore, the scalar product a.b is equal to 8.
To find the scalar product of two vectors a and b, you need to take the dot product of the two vectors. The dot product is calculated as the product of the corresponding components of the vectors, and then add them up.
Given that a = 2i + 3j + 4k and b = 5i - 2j + k, let's calculate the scalar product step by step.
1. Multiply the i-components:
a.i * b.i = 2 * 5 = 10
2. Multiply the j-components:
a.j * b.j = 3 * (-2) = -6
3. Multiply the k-components:
a.k * b.k = 4 * 1 = 4
4. Add up the products from steps 1, 2, and 3:
10 + (-6) + 4 = 8
Therefore, the scalar product of a and b is 8.