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Vector Algebra · Class 12 · CBSE · Science Mathematics

The vector projection of vec a=hat i+2hat j+2hat k on vec b=2hat i-hat j+2hat k is:

Practice question from Vector Algebra (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-3A7357

The vector projection of a⃗=i^+2j^+2k^\vec a=\hat i+2\hat j+2\hat k on b⃗=2i^−j^+2k^\vec b=2\hat i-\hat j+2\hat k is:

  1. A.43(2i^−j^+2k^)\frac{4}{3}(2\hat i-\hat j+2\hat k)
  2. B.49(2i^−j^+2k^)\frac{4}{9}(2\hat i-\hat j+2\hat k)Correct answer
  3. C.34(2i^−j^+2k^)\frac{3}{4}(2\hat i-\hat j+2\hat k)
  4. D.13(2i^−j^+2k^)\frac{1}{3}(2\hat i-\hat j+2\hat k)

Solution

The vector projection is proj⁡b⃗a⃗=a⃗⋅b⃗∣b⃗∣2b⃗\operatorname{proj}_{\vec b}\vec a=\frac{\vec a\cdot\vec b}{|\vec b|^2}\vec b. Here, a⃗⋅b⃗=4\vec a\cdot\vec b=4 and ∣b⃗∣2=9|\vec b|^2=9, giving proj⁡b⃗a⃗=49(2i^−j^+2k^)\operatorname{proj}_{\vec b}\vec a=\frac{4}{9}(2\hat i-\hat j+2\hat k).

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