If A = 5i + 12j and B = 12i - 5j, what is the scalar product A · B?
Practice Questions
1 question
Q1
If A = 5i + 12j and B = 12i - 5j, what is the scalar product A · B?
0
60
70
80
A · B = (5)(12) + (12)(-5) = 60 - 60 = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = 5i + 12j and B = 12i - 5j, what is the scalar product A · B?
Solution: A · B = (5)(12) + (12)(-5) = 60 - 60 = 0.
Steps: 8
Step 1: Identify the components of vector A. A = 5i + 12j means A has a component of 5 in the i direction and 12 in the j direction.
Step 2: Identify the components of vector B. B = 12i - 5j means B has a component of 12 in the i direction and -5 in the j direction.
Step 3: Write down the formula for the scalar product (dot product) of two vectors. The formula is A · B = (A_i * B_i) + (A_j * B_j), where A_i and A_j are the components of A, and B_i and B_j are the components of B.
Step 4: Substitute the components of A and B into the formula. A · B = (5 * 12) + (12 * -5).
Step 5: Calculate the first part: 5 * 12 = 60.
Step 6: Calculate the second part: 12 * -5 = -60.
Step 7: Add the results from Step 5 and Step 6: 60 + (-60) = 60 - 60 = 0.
Step 8: Conclude that the scalar product A · B is 0.
