CBSE  /  Class 12  /  Maths  /  Vector Algebra

  • 1. 
    If \(\vec{a}\) and \(\vec{b}\) are any two vector then (\(\vec{a}\) × \(\vec{b}\))² is equal to

  • (\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))²
  • (\(\vec{a}\))² (\(\vec{b}\))² + (\(\vec{a}\).\(\vec{b}\))²
  • (\(\vec{a}\).\(\vec{b}\))²
  • (\(\vec{a}\))²(\(\vec{b}\))²

  • 2. 
    If \(\hat{a}\) and \(\hat{b}\) be two unit vectors and 0 is the angle between them, then |\(\hat{a}\) – \(\hat{b}\)| is equal to

  • sin \(\frac{θ}{2}\)
  • 2 sin \(\frac{θ}{2}\)
  • cos \(\frac{θ}{2}\)
  • 2 cos \(\frac{θ}{2}\)

  • 3. 
    The angle between the vector 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) – \(\hat{k}\) is

  • \(\frac{π}{2}\)
  • \(\frac{π}{4}\)
  • \(\frac{π}{3}\)
  • 0

  • 4. 
    If \(\vec{a}\) = \(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) – \(\hat{k}\), \(\vec{c}\) = 3\(\hat{i}\) – p\(\hat{j}\) – 5\(\hat{k}\) are coplanar then P =

  • 6
  • -6
  • 2
  • -2

  • 5. 
    The distance of the point (- 3, 4, 5) from the origin

  • 50
  • 5√2
  • 6
  • None of these

  • 6. 
    If \(\vec{AB}\) = 2\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and the co-ordinates of A are (1, 2, -1) then coordinate of B are

  • (2, 2, -3)
  • (3, 2, -4)
  • (4, 2, -1)
  • (3, 3, -4)

  • 7. 
    If \(\vec{b}\) is a unit vector in xy-plane making an angle of \(\frac{π}{4}\) with x-axis. then \(\vec{b}\) is equal to

  • \(\hat{i}\) + \(\hat{j}\)
  • \(\vec{i}\) – \(\vec{j}\)
  • \(\frac{\vec{i}+\vec{j}}{√2}\)
  • \(\frac{\vec{i}-\vec{j}}{√2}\)

  • 8. 
    \(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) – 8\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) then the magnitude of \(\vec{a}\) + \(\vec{b}\) is equal to

  • 13
  • \(\frac{13}{4}\)
  • \(\frac{3}{13}\)
  • \(\frac{4}{13}\)

  • 9. 
    The vector in the direction of the vector \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\) that has magnitude 9 is

  • \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\)
  • \(\frac{\hat{i}-2\hat{j}+2\hat{k}}{3}\)
  • 3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))
  • 9(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))

  • 10. 
    The position vector of the point which divides the join of points 2\(\vec{a}\) – 3\(\vec{b}\) and \(\vec{a}\) + \(\vec{b}\) in the ratio 3 : 1 is

  • \(\frac{3\vec{a}-2\vec{b}}{2}\)
  • \(\frac{7\vec{a}-8\vec{b}}{2}\)
  • \(\frac{3\vec{a}}{2}\)
  • \(\frac{5\vec{a}}{4}\)
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