Question

If \( 2i\hat{i} - j\hat{j} - 3j\hat{k} \) and \( -3i\hat{i} + 4j\hat{j} - 4k\hat{k} \) are the position vectors of three points A, B, and C respectively, then \( \Delta ABC \) is:

• A. \( ABC \) is a right-angled triangle
• B. \( ABC \) is an isosceles triangle
• C. \( ABC \) are collinear points
• D. \( ABC \) is a scalene triangle

Hint:

For problems involving position vectors, calculate the distances between the points using the distance formula.

Answer 1

The Correct Option is D

By finding the magnitude of the vectors and applying the distance formula, we can conclude that \( \Delta ABC \) is a scalene triangle, as all the sides are of different lengths.