Question

Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).

• A. \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
• B. \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
• C. \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
• D. \(p = 0, \, q = 0\)

Hint:

Whenever the cross product of two vectors is zero, avoid expanding the entire determinant! Save time by directly writing the ratio of their corresponding components: \[ \frac{a_x}{b_x} = \frac{a_y}{b_y} = \frac{a_z}{b_z} \]

Answer 1

The Correct Option is B