CBSE  /  Class 12  /  Maths  /  Vector Algebra

  • 1. 
    The position vector of the point (1, 0, 2) is

  • \(\vec{i}\) +\(\vec{j}\) + 2\(\vec{k}\)
  • \(\vec{i}\) + 2\(\vec{j}\)
  • \(\vec{2}\) + 3\(\vec{k}\)
  • \(\vec{i}\) + 2\(\vec{K}\)

  • 2. 
    The modulus of 7\(\vec{i}\) – 2\(\vec{J}\) + \(\vec{K}\)

  • \(\sqrt{10}\)
  • \(\sqrt{55}\)
  • 3\(\sqrt{6}\)
  • 6

  • 3. 
    If O be the origin and \(\vec{OP}\) = 2\(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) and \(\vec{OQ}\) = 5\(\hat{i}\) + 4\(\hat{j}\) -3\(\hat{k}\), then \(\vec{PQ}\) is equal to

  • 7\(\hat{i}\) + 7\(\hat{j}\) – 7\(\hat{k}\)
  • -3\(\hat{i}\) + \(\hat{j}\) – \(\hat{k}\)
  • -7\(\hat{i}\) – 7\(\hat{j}\) + 7\(\hat{k}\)
  • 3\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

  • 4. 
    The scalar product of 5\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and 3\(\hat{i}\) – 4\(\hat{j}\) + 7\(\hat{k}\) is

  • 10
  • -10
  • 15
  • -15

  • 5. 
    If \(\vec{a}\).\(\vec{b}\) = 0, then

  • a ⊥ b
  • \(\vec{a}\) || \(\vec{b}\)
  • \(\vec{a}\) + \(\vec{b}\) = 0
  • \(\vec{a}\) – \(\vec{b}\) = 0

  • 6. 
    \(\vec{i}\) – \(\vec{j}\) =

  • 0
  • 1
  • \(\vec{k}\)
  • –\(\vec{k}\)

  • 7. 
    \(\vec{k}\) × \(\vec{j}\) =

  • 0
  • 1
  • \(\vec{i}\)
  • –\(\vec{i}\)

  • 8. 
    \(\vec{a}\). \(\vec{a}\) =

  • 0
  • 1
  • |\(\vec{a}\)|²
  • |\(\vec{a}\)|

  • 9. 
    The projection of the vector 2\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\) on the vector \(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\) is

  • \(\frac{4}{√6}\)
  • \(\frac{5}{√6}\)
  • \(\frac{4}{√3}\)
  • \(\frac{7}{√6}\)

  • 10. 
    If \(\vec{a}\) = \(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and b = 3\(\vec{i}\) + 2\(\vec{j}\) – \(\vec{k}\) then the value of (\(\vec{a}\) + 3\(\vec{b}\))(2\(\vec{a}\) – \(\vec{b}\))=. (a) 15

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