m=-2.00i+6.00j-4k and n=2.00i-3.00j. what is the dot product of m and n?
To find the dot product of two vectors, you need to multiply their corresponding components and then sum up the results.
Let's break down the given vectors:
Vector m: m = -2.00i + 6.00j - 4k
Vector n: n = 2.00i - 3.00j
Now, we can calculate the dot product using the formula:
m · n = (mₓ * nₓ) + (mᵧ * nᵧ) + (mᵤ * nᵤ)
Here, mₓ, mᵧ, and mᵤ represent the components of vector m, and nₓ, nᵧ represent the components of vector n. Since vector n does not have a component in the k direction, the k-component can be ignored.
Let's calculate the dot product step by step:
m ⋅ n = (-2.00 * 2.00) + (6.00 * -3.00) + (-4 * 0)
= (-4.00) + (-18.00) + 0
= -22.00
Therefore, the dot product of vectors m and n is -22.00.