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Question - 1

If \(\overrightarrow { a } \)is a non-zero  vector and m is a non-zero scalar then \(m\overrightarrow { a } \) is a unit vector if

  • A \(m=\pm 1\)
  • B \(a = \left| m \right| \)
  • C \(a = \frac { 1 }{ \left| m \right| } \)
  • D \(a = 1\)

Question - 2

If \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are unit vectors and \(\theta \) is the angle between them, then \((\overrightarrow { a } +\overrightarrow { b } )\) is a unit vector if

  • A  \( \theta = \frac { \pi }{ 3 } \)
  • B \(\theta = \frac { \pi }{ 4 } \)
  • C \(\theta = \frac { \pi }{ 2 } \)
  • D \(\theta = \frac {2 \pi }{ 3 } \)

Question - 3

If \(\overrightarrow { a } \) and \(\overrightarrow { b } \) include an angle \({ 120 }^{ \circ }\) and their magnitude are\( 2\) and \(\sqrt { 3 } \) then \(\overrightarrow { a } . \overrightarrow { b } \) is equal to

  • A \(\sqrt { 3 } \)
  • B \(- \sqrt { 3 } \)
  • C \(2\)
  • D \(\frac { -\sqrt { 3 } }{ 2 }\)

Question - 4

If \(\overrightarrow { u } \ =\overrightarrow {a} \times (\overrightarrow {b}\times\overrightarrow {c})+\overrightarrow b \times (\overrightarrow c \times \overrightarrow a) + \overrightarrow {c} (\overrightarrow a \times\overrightarrow b)\) , then

  • A \(\overrightarrow { u }\) is a unit vector
  • B \(\overrightarrow { u } = \overrightarrow { a }+ \overrightarrow { b }+\overrightarrow { c }\)
  • C \(\overrightarrow { u } = \overrightarrow { 0 }\)
  • D \(\overrightarrow { u } \neq \overrightarrow { 0 }\)

Question - 5

If \(\overrightarrow { a } +\overrightarrow { b } +\overrightarrow { c } =0\),\(\left| \overrightarrow { a } \right| = 3\) , \(\left| \overrightarrow { b }\right| = 4\) , \(\left| \overrightarrow { c }\right| = 5\) then the angle between \(\overrightarrow { a }\) and \(\overrightarrow { b }\) is ,

  • A \(\theta = \frac { \pi }{ 6 } \)
  • B \(\theta = \frac { 2\pi }{ 3 }\)
  • C \(\theta = \frac { 5\pi }{ 3 }\)
  • D \(\theta = \frac { \pi }{ 2 }\)

Question - 6

The vectors \(2\overrightarrow { i }+3\overrightarrow { j }+4\overrightarrow { k }\) and \(a\overrightarrow { i }+b\overrightarrow { j }+c\overrightarrow { k }\) are perpendicular when

  • A \(a=2 \ , \ b=3 \ , \ c=-4\)
  • B \(a=4 \ , \ b=4 \ , \ c=5\)
  • C \(a=4 \ , \ b=4 \ , \ c=-5\)
  • D \(a=-2 \ , \ b=3 \ ,\ c=4\)

Question - 7

The area of the parallelogram having a diagonal \(3\overrightarrow { i }+\overrightarrow { j }-\overrightarrow { k }\) and a side \(\overrightarrow { i }-3\overrightarrow { j }+4\overrightarrow { k }\) is ,

  • A \(10\sqrt { 3 }\)
  • B \(5\sqrt { 30 }\)
  • C \(\frac { 3 }{ 2 } \sqrt { 30}\)
  • D \(3\sqrt { 30}\)

Question - 8

If \(\left| \overrightarrow { a }+\overrightarrow { b } \right| = \left| \overrightarrow {a} - \overrightarrow {b} \right|\) then

  • A \(\overrightarrow { a }\) is parallel to \(\overrightarrow { b }\)
  • B \(\overrightarrow { a }\) is perpendicular to \(\overrightarrow { b }\)
  • C \( \left| \overrightarrow { a }\right| = \left| \overrightarrow { b }\right|\)
  • D \(\overrightarrow { a }\) and \(\overrightarrow { b }\) are unit vectors

Question - 9

If \(\overrightarrow { p }\) and \(\overrightarrow { q }\) and \(\overrightarrow { p }+\overrightarrow { q }\) are vectors of magnitude \(\lambda \) then the magnitude of \(\left| \overrightarrow { p }-\overrightarrow { q } \right|\) is

  • A \(2\lambda \)
  • B \(\sqrt { 3 }\lambda\)
  • C \(\sqrt { 2 }\lambda\)
  • D \(1\)

Question - 10

If \(\overrightarrow { a } \times (\overrightarrow b\times \overrightarrow c) +\overrightarrow b \times (\overrightarrow c \times \ \overrightarrow a) + \overrightarrow c (\overrightarrow a \times \overrightarrow b) = \overrightarrow x \times \overrightarrow y\)then

  • A \(\overrightarrow { x }=\overrightarrow { 0 }\)
  • B \(\overrightarrow { y }=\overrightarrow { 0 }\)
  • C \(\overrightarrow { x }\) and \(\overrightarrow { y }\) are parallel
  • D \(\overrightarrow { x }=\overrightarrow { 0 }\) or  \(\overrightarrow { y } =\overrightarrow { 0 }\) or \(\overrightarrow { x }\) and \(\overrightarrow { y }\) are parallel
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