Question

If vector equation of the line \( \frac{x-2}{2} = \frac{2y-5}{-3} = z+1 \), is \[ \mathbf{r} = \left( 2\hat{i} + \frac{5}{2} \hat{j} - k \right) + \lambda \left( 2\hat{i} - \frac{3}{2} \hat{j} + p \hat{k} \right) \] then \( p \) is equal to:

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

For vector equations, equating the coefficients of the unit vectors gives the required values for constants.

Answer 1

The Correct Option is A

From the given vector equation, equate the components of the vector to find the value of \( p \). The solution leads to \( p = 0 \).
Final Answer: \[ \boxed{0} \]