Scalar Triple Product

Step 1: Concept
Since is perpendicular to both and , it must be parallel to their cross product \vec{\delta} = \lambda(5\hat{i} - 5\hat{j} - 5\hat{k}) = 5\lambda(\hat{i} - \hat{j} - \hat{k}) \vec{\delta} \cdot \vec{\gamma} = 10 \lambda \vec{\delta} = 5(-2/5)(\hat{i} - \hat{j} - \hat{k}) = -2\hat{i} + 2\hat{j} + 2\hat{k} |\vec{\delta}| = \sqrt{(-2)^2 + 2^2 + 2^2} = \sqrt{4 + 4 + 4} = \sqrt{12} = 2\sqrt{3}$. Final Answer:(A)

Step 1: Concept
Use Vector Triple Product expansion: .
Step 2: Analysis
.
Comparing coefficients: and .
or depending on sign orientation.
Step 3: Conclusion
The angle is . Final Answer:(D)