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BITSAT2018MathematicsVector AlgebraActual

If h is the altitude of a parallelopiped determined by the vectors a ^ , b ^ , c ^ and the base is taken to be the parallelogram determined by a ^ and b ^ where a ^ = i ^ + j ^ + k ^ , b ^ = 2 i ^ + 4 j ^ - k ^ and c ^ = i ^ + j ^ + 3 k ^ , then the value of 19 h 2 is

Options

  1. A19
  2. B16
  3. C8
  4. DNone of these

Correct answer

C. 8

Step-by-step solution

Volume of the parallelopiped = a ^   b ^   c ^ ⇒ (area of the base parallelogram) × h = a ^   b ^   c ^ ⇒ a ^ × b ^ h = a ^   b ^   c ^ ⇒ - 5 i ^ + 3 j ^ + 2 k ^ h = 1 1 1 2 4 - 1 1 1 3 ⇒ 38 h = 4 ⇒ h = 4 38 ⇒ 38 h 2 = 4 2 ⇒ 19 h 2 = 8 Hence, option (c) is correct.

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