If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and

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Question: If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?

Options:

Correct Answer: 180 degrees

Solution:

A · B = 5*5 + 12*(-12) = 25 - 144 = -119. Since A · B < 0, angle is 180 degrees.

If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?

If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?

Step 1: Identify the components of vector A and vector B. Vector A = 5i + 12j and vector B = 5i - 12j.
Step 2: Calculate the dot product of vectors A and B using the formula A · B = Ax * Bx + Ay * By.
Step 3: Substitute the values into the dot product formula: A · B = (5 * 5) + (12 * -12).
Step 4: Calculate the products: 5 * 5 = 25 and 12 * -12 = -144.
Step 5: Add the results of the products: 25 + (-144) = 25 - 144 = -119.
Step 6: Determine the angle based on the dot product result. Since A · B is less than 0 (A · B < 0), the angle between A and B is 180 degrees.

Dot Product – The dot product of two vectors is calculated as A · B = |A||B|cos(θ), where θ is the angle between the vectors.
Angle Calculation – The angle between two vectors can be determined using the dot product and the magnitudes of the vectors.
Vector Components – Understanding vector components in terms of i and j helps in visualizing and calculating angles.