CBSE  /  Class 12  /  Maths  /  Vector Algebra

  • 1. 
    If \(\vec{a}\) = \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = 2\(\hat{i}\) – 4\(\hat{k}\), \(\vec{c}\) =\(\hat{i}\) + λ\(\hat{j}\) + 3\(\hat{j}\) are coplanar, then the value of λ is

  • \(\frac{5}{2}\)
  • \(\frac{3}{5}\)
  • \(\frac{7}{3}\)
  • –\(\frac{5}{3}\)

  • 2. 
    The vectors \(\vec{a}\) = x\(\hat{i}\) – 2\(\hat{j}\) + 5\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + y\(\hat{j}\) – z\(\hat{k}\) are collinear, if

  • x = 1, y = -2, z = -5
  • x = \(\frac{3}{2}\), y = -4, z = -10
  • x = \(\frac{3}{2}\), y = 4, z = 10
  • All of these

  • 3. 
    The vectors (x, x + 1, x + 2), (x + 3, x + 4, x + 5) and (x + 6, x + 7, x + 8) are coplanar for

  • all values of x
  • x < 0
  • x ≤ 0
  • None of these

  • 4. 
    The vectors \(\vec{AB}\) = 3\(\hat{i}\) +4\(\hat{k}\) and \(\vec{AC}\) = 5\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) are the sides of ΔABC. The length of the median through A is

  • \(\sqrt{18}\)
  • \(\sqrt{72}\)
  • \(\sqrt{33}\)
  • \(\sqrt{288}\)

  • 5. 
    The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is

  • √3
  • 1 – √3
  • 1 + √3
  • -√3
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