A times B = |i A_x B_x j A_y B_y k A_z B_z| Sample: Vector Product: A = 2i + j B

Question

A times B = |i A_x B_x j A_y B_y k A_z B_z| Sample: Vector Product: A = 2i + j B = i + 3j A times B = |i 2 1 j 1 3 k 0 0| = (6 - 1) k = 5k If A and B are in x-y plane, A times B is along the + z direction theta is the angle formed by AB: sin theta = |C|/|A||B| Given: |A| = squareroot 5 |B| = squareroot 10 |C| = 5 sin theta = 5/(squareroot 5 times squareroot 10) = 5 c. the Right-Hand Rule gives the vector e B. Trigonometry Basic relations for a triangle sin theta = y/r cos theta = x/r tan theta = y/x = sin/cos sin^2 + cos^2 = 1 Sin and Cos waves

Explanation / Answer

suppose you are taking i close that row and column so remaining will be 1*0-3*0 similarly for j 2*0-1*0 and for k 2*3-1*1 so finally i(1-0)-j(0-0)+ k(6-1)= 0+0+ 5k = 5k

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