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JEE MainMathematicsVector Algebra

Let p = i + j and q = i - k be two vectors. Let v be a vector coplanar with p and q , such that v is orthogonal to p . If v q = 6 , then the value of | v q |^2 is equal to

Options

  1. A8
  2. B12
  3. C6
  4. D36

Correct answer

B. 12

Step-by-step solution

Let v = x p + y q since v is coplanar with p and q . Given p = i + j and q = i - k . We have | p |^2 = 2 , | q |^2 = 2 , and p q = 1 . Since v is orthogonal to p , we have v p = 0 . (x p + y q ) p = x| p |^2 + y( p q ) = 0 2x + y = 0 y = -2x Also given v q = 6 . (x p + y q ) q = x( p q ) + y| q |^2 = 6 x(1) + y(2) = 6 Substituting y = -2x into the above equation: x + 2(-2x) = 6 -3x = 6 x = -2 We need to find | v q |^2 . v q = (x p + y q ) q = x( p q ) + y( q q ) = x( p q ) | v q |^2 = x^2 | p q |^2 Now, p q = ( i +

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