Let Vector "A" Cross With Vector "B" Equal To Ten,then Find (A+B) Cross With (A-B) ?
What is Tilili?
(A+B)x(A-B) = AxA + BxA - AxB - BxB
= BxA - AxB
= -2(AxB)
But, AxB is a vector, not a scalar. You have a glitch in there somewhere.
To find the cross product of vectors (A + B) and (A - B), we need to calculate the cross product separately for (A + B) and (A - B) and then subtract one from the other.
The cross product of two vectors (let's say Vector C and Vector D) is calculated using the following formula:
C x D = |C| |D| sin(theta) n
Where:
- C x D represents the cross product of vectors C and D.
- |C| and |D| represent the magnitudes (or lengths) of vectors C and D, respectively.
- sin(theta) represents the sine of the angle (theta) between vectors C and D.
- n represents the unit vector normal to the plane formed by vectors C and D.
Now, let's apply this formula to calculate the cross products for (A + B) and (A - B).
Given that the cross product of Vector A and Vector B is 10, we have:
A x B = 10
First, let's calculate (A + B):
(A + B) x (A - B) = (A x A) - (A x B) + (B x A) - (B x B)
Since the cross product of a vector with itself is zero, (A x A) and (B x B) will be zero.
So, the formula simplifies to:
(A + B) x (A - B) = - (A x B) + (B x A)
Since we know that A x B = 10, the equation becomes:
(A + B) x (A - B) = -10 + (B x A)
To find (B x A), we note that the cross product is anti-commutative, meaning that the order of vectors matters. It can be written as:
(B x A) = -(A x B)
Therefore, the equation simplifies further to:
(A + B) x (A - B) = -10 - (A x B)
Since A x B = 10, the equation becomes:
(A + B) x (A - B) = -10 - 10
= -20
Hence, the cross product of (A + B) and (A - B) is -20.