Question

The dot product of a vector with the vectors \( \mathbf{i} + \mathbf{j} - 3\mathbf{k} \), \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k} \) and \( 2\mathbf{i} + \mathbf{j} + 4\mathbf{k} \) are 0, 5 and 8 respectively. The vector is:

• A. \(\hat i+2\hat j+\hat k\)
• B. \(-\hat i+3\hat j-2\hat k\)
• C. \(\hat i+2\hat j+3\hat k\)
• D. i-3 j-3 k

Hint:

Dot products give linear equations in components.

Answer 1

The Correct Option is C

Let v=(x,y,z). Solve the linear system from dot products to get (x,y,z)=(1,2,3).