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Class 12

Scalar and Vector Products, with Mixed Practice — Quiz

Five questions on scalar and vector products. Pick one answer for each.

5 questions, one mark each. 3 to pass. Suggested time: 10 minutes. Your answers are not recorded.

  1. Find a⃗⋅b⃗\vec a \cdot \vec b for a⃗=i^+2j^−k^\vec a = \hat i + 2\hat j - \hat k and b⃗=3i^−j^+2k^\vec b = 3\hat i - \hat j + 2\hat k.
  2. For what λ\lambda are λi^+2j^+k^\lambda\hat i + 2\hat j + \hat k and 2i^−3j^+4k^2\hat i - 3\hat j + 4\hat k perpendicular?
  3. Find the projection of a⃗=4i^+j^+k^\vec a = 4\hat i + \hat j + \hat k on b⃗=2i^−j^+2k^\vec b = 2\hat i - \hat j + 2\hat k.
  4. Find a⃗×b⃗\vec a \times \vec b for a⃗=i^+j^\vec a = \hat i + \hat j and b⃗=j^+k^\vec b = \hat j + \hat k.
  5. Find the area of the parallelogram with adjacent sides i^+2j^\hat i + 2\hat j and 3i^+j^3\hat i + \hat j.
Unanswered questions are marked wrong.

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