Which one of the following can be written for (\(\vec{a}\) – \(\vec{b}\)) × (\(\vec{a}\) + \(\vec{b}\))
  • \(\vec{a}\) × \(\vec{b}\)
  • 2\(\vec{a}\) × \(\vec{b}\)
  • \(\vec{a}\)² – \(\vec{b}\)
  • 2\(\vec{b}\) × \(\vec{b}\)
The points with position vectors (6), (1, 2) and (a, 10) are collinear if the of a is
  • -8
  • 4
  • 3
  • 12
|\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
  • \(\frac{π}{2}\)
  • 0
  • \(\frac{π}{4}\)
  • \(\frac{π}{6}\)
|\(\vec{a}\) × \(\vec{b}\)| = |\(\vec{a}\).\(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
  • 0
  • \(\frac{π}{2}\)
  • \(\frac{π}{4}\)
  • π
If ABCDEF is a regular hexagon then \(\vec{AB}\) + \(\vec{EB}\) + \(\vec{FC}\) equals
  • zero
  • 2\(\vec{AB}\)
  • 4\(\vec{AB}\)
  • 3\(\vec{AB}\)
Which one of the following is the modulus of x\(\hat{i}\) + y\(\hat{j}\) + z\(\hat{k}\)?
  • \(\sqrt{x^2+y^2+z^2}\)
  • \(\frac{1}{\sqrt{x^2+y^2+z^2}}\)
  • x² + y² + z²
  • none of these
If C is the mid point of AB and P is any point outside AB then,
  • \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\)
  • \(\vec{PA}\) + \(\vec{PB}\) = \(\vec{PC}\)
  • \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\) = 0
  • None of these
If \(\vec{OA}\) = 2\(\vec{i}\) – \(\vec{j}\) + \(\vec{k}\), \(\vec{OB}\) = \(\vec{i}\) – 3\(\vec{j}\) – 5\(\vec{k}\) then |\(\vec{OA}\) × \(\vec{OB}\)| =
  • 8\(\vec{i}\) + 11\(\vec{j}\) – 5\(\vec{k}\)
  • \(\sqrt{210}\)
  • sin θ
  • \(\sqrt{40}\)
If |a| = |b| = |\(\vec{a}\) + \(\vec{b}\)| = 1 then |\(\vec{a}\) – \(\vec{b}\)| is equal to
  • 1
  • √3
  • 0
  • None of these
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
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 \(\frac{θ}{2}\)
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
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
The distance of the point (- 3, 4, 5) from the origin
  • 50
  • 5√2
  • 6
  • None of these
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)
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
  • \(\hat{i}\) + \(\hat{j}\)
  • \(\vec{i}\) – \(\vec{j}\)
  • \(\frac{\vec{i}+\vec{j}}{√2}\)
  • \(\frac{\vec{i}-\vec{j}}{√2}\)
\(\vec{a}\) = 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
  • \(\frac{13}{4}\)
  • \(\frac{3}{13}\)
  • \(\frac{4}{13}\)
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\(\hat{k}\))
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
  • \(\frac{3\vec{a}-2\vec{b}}{2}\)
  • \(\frac{7\vec{a}-8\vec{b}}{2}\)
  • \(\frac{3\vec{a}}{2}\)
  • \(\frac{5\vec{a}}{4}\)
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\(\hat{k}\)
  • \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)
0 h : 0 m : 1 s

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