CBSE  /  Class 12  /  Maths  /  Vector Algebra

  • 1. 
    The vector having, initial and terminal points as (2, 5, 0) and (- 3, 7, 4) respectively is

  • –\(\hat{i}\) + 12\(\hat{j}\) + 4\(\hat{k}\)
  • 5\(\hat{i}\) + 2\(\hat{j}\) – 4\(\hat{k}\)
  • -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)
  • \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

  • 2. 
    Find the value of λ such that the vectors \(\vec{a}\) = 2\(\hat{i}\) + λ\(\hat{j}\) + \(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) + 3\(\hat{k}\) are orthogonal

  • 0
  • 1
  • \(\frac{3}{2}\)
  • –\(\frac{5}{2}\)

  • 3. 
    The value of λ for which the vectors 3\(\hat{i}\) – 6\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – 4\(\hat{j}\) + λ\(\hat{k}\) are parallel is

  • \(\frac{2}{3}\)
  • \(\frac{3}{2}\)
  • \(\frac{5}{2}\)
  • –\(\frac{2}{5}\)

  • 4. 
    The vectors from origin to the points A and B are \(\vec{a}\) = 2\(\hat{i}\) – 3\(\hat{j}\) +2\(\hat{k}\) and \(\vec{b}\) = 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) respectively, then the area of triangle OAB is

  • 340
  • \(\sqrt{25}\)
  • \(\sqrt{229}\)
  • \(\frac{1}{2}\) \(\sqrt{229}\)

  • 5. 
    For any vector \(\vec{a}\) the value of (\(\vec{a}\) × \(\vec{i}\))² + (\(\vec{a}\) × \(\hat{j}\))² + (\(\vec{a}\) × \(\hat{k}\))² is equal to

  • \(\vec{a}\)²
  • 3\(\vec{a}\)²
  • 4\(\vec{a}\)²
  • 2\(\vec{a}\)²

  • 6. 
    If |\(\vec{a}\)| = 10, |\(\vec{b}\)| = 2 and \(\vec{a}\).\(\vec{b}\) = 12, then the value of |\(\vec{a}\) × \(\vec{b}\)| is

  • 5
  • 10
  • 14
  • 16

  • 7. 
    The vectors λ\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\), \(\hat{i}\) + λ\(\hat{j}\) – \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) + λ\(\hat{k}\) are coplanar if

  • λ = -2
  • λ = 0
  • λ = 1
  • λ = -1

  • 8. 
    If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are unit vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = \(\vec{0}\), then the value of \(\vec{a}\).\(\vec{b}\) + \(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\)

  • 1
  • 3
  • –\(\frac{3}{2}\)
  • None of these

  • 9. 
    Projection vector of \(\vec{a}\) on \(\vec{b}\) is

  • (\(\frac{\vec{a}.\vec{b}}{|\vec{b}|^2}\))\(\vec{b}\)
  • \(\frac{\vec{a}.\vec{b}}{|\vec{b}|}\)
  • \(\frac{\vec{a}.\vec{b}}{|\vec{a}|}\)
  • (\(\frac{\vec{a}.\vec{b}}{|\vec{a}|^2}\))\(\hat{b}\)

  • 10. 
    If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = 5 and |\(\vec{a}\)| = 2, |\(\vec{b}\)| = 3, |\(\vec{c}\)| = 5, then the value of \(\vec{a}\).\(\vec{b}\) +\(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\) is

  • 0
  • 1
  • -19
  • 38
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