If C⃗ = -5 i^ - 3 j^ - 4 k^, what is C⃗ × j^?
+i +j +k
-5 -3 -4
+0 +1 +0
= 5 k + 4 i
or
4i +0j +5k
(note obviously perpendicular to j so no j component)
To find the cross product of two vectors, we can use the following formula:
A × B = (AyBz - AzBy)i^ + (AzBx - AxBz)j^ + (AxBy - AyBx)k^
In this case, we have:
C⃗ = -5i^ - 3j^ - 4k^
j^ = 0i^ + 1j^ + 0k^
Using the formula, we can substitute the values into the equation to find the cross product:
C⃗ × j^ = ((-3)(0) - (-4)(1))i^ + ((-4)(0) - (-5)(0))j^ + ((-5)(1) - (-3)(0))k^
Simplifying the equation, we get:
C⃗ × j^ = -4i^ + 0j^ + (-5)k^
Therefore, the cross product of C⃗ and j^ is -4i^ - 5k^.