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\(\vec{K}\)
The modulus of 7\(\vec{i}\) – 2\(\vec{J}\) + \(\vec{K}\)
  • \(\sqrt{10}\)
  • \(\sqrt{55}\)
  • 3\(\sqrt{6}\)
  • 6
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\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)
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
If \(\vec{a}\).\(\vec{b}\) = 0, then
  • a ⊥ b
  • \(\vec{a}\) || \(\vec{b}\)
  • \(\vec{a}\) + \(\vec{b}\) = 0
  • \(\vec{a}\) – \(\vec{b}\) = 0
\(\vec{i}\) – \(\vec{j}\) =
  • 0
  • 1
  • \(\vec{k}\)
  • –\(\vec{k}\)
\(\vec{k}\) × \(\vec{j}\) =
  • 0
  • 1
  • \(\vec{i}\)
  • –\(\vec{i}\)
\(\vec{a}\). \(\vec{a}\) =
  • 0
  • 1
  • |\(\vec{a}\)|²
  • |\(\vec{a}\)|
The projection of the vector 2\(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\) on the vector \(\hat{i}\) – 2\(\hat{j}\) + \(\hat{k}\) is
  • \(\frac{4}{√6}\)
  • \(\frac{5}{√6}\)
  • \(\frac{4}{√3}\)
  • \(\frac{7}{√6}\)
If |\(\vec{a}\)|= \(\sqrt{26}\), |b| = 7 and |\(\vec{a}\) × \(\vec{b}\)| = 35, then \(\vec{a}\).\(\vec{b}\) =
  • 8
  • 7
  • 9
  • 12
If \(\vec{a}\) = 2\(\vec{i}\) – 3\(\vec{j}\) + 4\(\vec{k}\) and \(\vec{b}\) = \(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\) + \(\vec{b}\) =
  • \(\vec{i}\) + \(\vec{j}\) + 3\(\vec{k}\)
  • 3\(\vec{i}\) – \(\vec{j}\) + 5\(\vec{k}\)
  • \(\vec{i}\) – \(\vec{j}\) – 3\(\vec{k}\)
  • 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\)
If \(\vec{a}\) = \(\vec{i}\) + 2\(\vec{j}\) + 3\(\vec{k}\) and \(\vec{b}\) = 3\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\), then cos θ =
  • \(\frac{6}{7}\)
  • \(\frac{5}{7}\)
  • \(\frac{4}{7}\)
  • \(\frac{1}{2}\)
If |\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)|, then
  • \(\vec{a}\) || \(\vec{a}\)
  • \(\vec{a}\) ⊥ \(\vec{b}\)
  • |\(\vec{a}\)| = |\(\vec{b}\)|
  • None of these
The projection of the vector 2\(\hat{i}\) + 3\(\hat{j}\) – 6\(\hat{k}\) on the line joining the points (3, 4, 2) and (5, 6,3) is
  • \(\frac{2}{3}\)
  • \(\frac{4}{3}\)
  • –\(\frac{4}{3}\)
  • \(\frac{5}{3}\)
If |\(\vec{a}\) × \(\vec{b}\)| – |\(\vec{a}\).\(\vec{b}\)|, then the angle between \(\vec{a}\) and \(\vec{b}\), is
  • 0
  • \(\frac{π}{2}\)
  • \(\frac{π}{4}\)
  • π
The angle between two vector \(\vec{a}\) and \(\vec{b}\) with magnitude √3 and 4, respectively and \(\vec{a}\).\(\vec{b}\) = 2√3 is
  • \(\frac{π}{6}\)
  • \(\frac{π}{3}\)
  • \(\frac{π}{2}\)
  • \(\frac{5π}{2}\)
Unit vector perpendicular to each of the vector 3\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\) and 2\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) is
  • \(\frac{\hat{i}+\hat{j}+\hat{k}}{√3}\)
  • \(\frac{\hat{i}-\hat{j}+\hat{k}}{√3}\)
  • \(\frac{\hat{i}-\hat{j}-\hat{k}}{√3}\)
  • \(\frac{\hat{i}+\hat{j}-\hat{k}}{√3}\)
If \(\vec{a}\) = 2\(\vec{i}\) – 5\(\vec{j}\) + k and \(\vec{b}\) = 4\(\vec{i}\) + 2\(\vec{j}\) + \(\vec{k}\) then \(\vec{a}\).\(\vec{b}\) =
  • 0
  • -1
  • 1
  • 2
If 2\(\vec{i}\) + \(\vec{j}\) + \(\vec{k}\), 6\(\vec{i}\) – \(\vec{j}\) + 2\(\vec{k}\) and 14\(\vec{i}\) – 5\(\vec{j}\) + 4\(\vec{k}\) be the position vector of the points A, B and C respectively, then
  • The A, B and C are collinear
  • A, B and C are not colinear
  • \(\vec{AB}\) ⊥ \(\vec{BC}\)
  • None of these
According to the associative lass of addition of addition of s ector
  • \(\vec{b}\), \(\vec{a}\)
  • \(\vec{a}\), \(\vec{b}\)
  • \(\vec{a}\), 0
  • \(\vec{b}\), 0
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