Consider the two vectors m~ = (a,
b.= aˆı+bˆ and n~ = (c,
d.= cˆı + dˆ, where a = 4, b = 4, c = 2, and d = −2. a and c represent the x-displacement and b and d represent the ydisplacement in a cartesian xy coordinate system. what is the magnitude of the vector product m~ × m~ ?

0

Step-by-step explanation:

We are given the following vectors:

m = (a, b) = ai + bj

n = (c, d) = ci + dj

Values of a,b,c and d are given to be: a = 4, b = 4, c = 2, and d = −2

So, the vectors we have will be:

m = (4, 4) = 4i + 4j

n = (2, -2) = 2i - 2j

We need to find the magnitude of vector product m x m.

Remember that the vector(cross) product of a vector with itself is always 0. For any two vectors A and B, the magnitude of their vector(cross) product is defined as:

A x B = AB sin(θ)

Here, θ is the angle between two vectors A and B. if A and B represent the same vector then the angle θ will be zero. Since sin(θ) = 0, the magintude of the vector product will also be 0.

Therefore, for our question, the magnitude of the vector product m x m will be equal to 0.

step-by-step :