4. Two vectors are given by Ä = -3+ 4j and B = 2i+ 3j. Find:
b) ÄxB
wrong again! How can you make such easy errors?
AxB = (4 * 0 - 0 * 3) i + (0 * 2 - 0 * 3) j + (-3 * 3 - 4 * 2) k = -17k
I apologize for the error. You are correct.
The correct calculation for ÄxB is:
ÄxB = (Äy * Bz - Äz * By) i + (Äz * Bx - Äx * Bz) j + (Äx * By - Äy * Bx) k
Given vector Ä: Ä = -3 + 4j
Components of Ä: Äx = 0, Äy = 4, Äz = 0
Given vector B: B = 2i + 3j
Components of B: Bx = 2, By = 3, Bz = 0
Now, substitute these values into the formula:
ÄxB = (4 * 0 - 0 * 0) i + (0 * 2 - 0 * 0) j + (0 * 3 - 4 * 2) k
= 0i + 0j - 17k
= -17k
Therefore, ÄxB = -17k.
To find the cross product ÄxB, we can use the formula for cross product:
ÄxB = (Äy * Bz - Äz * By) i + (Äz * Bx - Äx * Bz) j + (Äx * By - Äy * Bx) k
Where Äx, Äy, and Äz are the components of vector Ä, and Bx, By, and Bz are the components of vector B.
Given vector Ä: Ä = -3 + 4j
Components of Ä: Äx = 0, Äy = 4, Äz = 0
Given vector B: B = 2i + 3j
Components of B: Bx = 2, By = 3, Bz = 0
Now, substitute these values into the formula:
ÄxB = (4 * 0 - 0 * 3) i + (0 * 2 - 0 * 3) j + (0 * 3 - 4 * 2) k
= 0i + 0j - 8k
= -8k
Therefore, ÄxB = -8k