Cross product of vector:
If axb(cross product)=(2,0,1) and bxc= -4,0,-4
solve magnitude of axb times magnitude of b x c
|a x b| x|bxc|
|(2,0,1)| = √(4+0+1) = √5
|(-4,0,-4)| = √(16+0+16) = √32
so their product is √5√32 = √60 = 2√15
To solve for the magnitude of (a x b) times the magnitude of (b x c), we will first find the magnitudes of (a x b) and (b x c), and then multiply them together.
Step 1: Finding the magnitude of (a x b)
Given that (a x b) = (2, 0, 1), we can find its magnitude using the formula:
|a x b| = sqrt((a x b)^2)
= sqrt(2^2 + 0^2 + 1^2)
= sqrt(4 + 0 + 1)
= sqrt(5)
So, the magnitude of (a x b) is sqrt(5).
Step 2: Finding the magnitude of (b x c)
Given that (b x c) = (-4, 0, -4), we can find its magnitude using the same formula:
|b x c| = sqrt((-4)^2 + 0^2 + (-4)^2)
= sqrt(16 + 0 + 16)
= sqrt(32)
= 4sqrt(2)
So, the magnitude of (b x c) is 4sqrt(2).
Step 3: Calculating the product of the magnitudes
Finally, we can calculate the product of the magnitudes:
|a x b| x |b x c| = sqrt(5) x 4sqrt(2)
To multiply two square roots, we can simply multiply the numbers inside the square roots:
sqrt(5) x 4sqrt(2) = 4 x sqrt(5) x sqrt(2)
= 4 x sqrt(10)
Therefore, the magnitude of (a x b) times the magnitude of (b x c) is 4sqrt(10).