Hello, I have the answer to part a. already. All i need is part b. just part b.

Question

Hello,

I have the answer to part a. already. All i need is part b. just part b.

Consider three arbitrary vectors in the Cartesian coordinate system: A = (A_x, A_y, A_z), B = (B_x, B_y, B_z) and C = (C_x, C_y, C_z), Prove the following relation (back cab rule): A times (B times C) = B (A middot B) - C (A middot B) Use the back cap rule verified above to show that the general solution of the vector equation C = A times X, where A is a known vector and X an unknown vector, is X = (C times A)/(A middot A) + k A, when two vectors, A and C, are perpendicular with each other.

Explanation / Answer

Let theta be angle between A and C .

Thus, theta = 90 degree

As, C = A * X

Thus, X = (C * A * sin(theta))/A2 + kA

                =   (C X A)/(A.A) + kA

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