ExamBro
ExamBro
AP EAMCET · Maths · Vector Algebra

If \(\bar{u}, \bar{v}, \bar{w}\) are non coplanar vectors and \(p, q\) are real numbers, then the equality \(\left[\begin{array}{lll}3 \overline{\mathrm{u}} & \mathrm{p} \overline{\mathrm{v}} & \mathrm{p} \overline{\mathrm{w}}\end{array}\right]-\left[\begin{array}{lll}\mathrm{p} \overline{\mathrm{v}} & \overline{\mathrm{w}} & \mathrm{q} \overline{\mathrm{u}}\end{array}\right]-\left[\begin{array}{lll}2 \overline{\mathrm{w}} & \mathrm{q} \overline{\mathrm{v}} & \mathrm{q} \overline{\mathrm{u}}\end{array}\right]=0\) holds for

  1. A exactly one ordered pair of (p,q)
  2. B exactly two ordered pairs of (p,q)
  3. C all ordered pairs of (p,q)
  4. D no ordered pair of (p,q)
Verified Solution

Answer & Solution

Correct Answer

(A) exactly one ordered pair of (p,q)

Step-by-step Solution

Detailed explanation

\( \left[3 \overline{\mathrm{u}} \ \mathrm{p} \overline{\mathrm{v}} \ \mathrm{p} \overline{\mathrm{w}}\right] = 3p^2 [\overline{\mathrm{u}} \ \overline{\mathrm{v}} \ \overline{\mathrm{w}}] \)…