Question

If \( \mathbf{a} = i + 2j + 3k \), \( \mathbf{b} = i + 2j + k \), and \( \mathbf{c} = 3i + j \), then \( \mathbf{a} + \mathbf{b} \) is at right angle to \( \mathbf{c} \), then \( a + b \) and \( t \) are equal to:

• A. 4
• B. 6
• C. 2
• D. 3

Hint:

Vectors are perpendicular if their dot product equals zero. Use this property to find the angle between vectors.

Answer 1

The Correct Option is A

Step 1: Check for perpendicular vectors. To check whether two vectors are perpendicular, take the dot product and set it equal to zero. Solve the resulting equations for the magnitude and the value of \( t \).
Step 2: Conclusion. Thus, the value of \( a + b \) and \( t \) is 4.