12th Standard cbse -- Maths - Vector Algebra

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Question - 1

A vector equally inclined to axes is

  • A \(\widehat { i } +\widehat { j } +\widehat { k } \)
  • B \(\widehat { i } -\widehat { j } +\widehat { k } \)
  • C \(\widehat { i } -\widehat { j } -\widehat { k } \)
  • D \(-\widehat { i } +\widehat { j } -\widehat { k } \)

Question - 2

The position vector of a point which divides the join of points with position vectors \(\vec { a } +\vec { b } \) and \(2\vec { a } -\vec { b } \) in the ratio 1:2 internally is

  • A \(\frac { 3\vec { a } +a\vec { b } }{ 3 } \)
  • B \(\vec { a } \)
  • C \(\frac { 5\vec { a } -\vec { b } }{ 3 } \)
  • D \(\frac { 4\vec { a } +\vec { b } }{ 3 } \)

Question - 3

A vector in the direction of vector \(\widehat { i } -2\widehat { j } +\widehat { k } \) that has magnitude 15 is

  • A \(\frac { \widehat { i } -2\widehat { j } +2\widehat { k } }{ 3 } \)
  • B \(15\widehat { i } -30\widehat { j } +30\widehat { k } \)
  • C \(\widehat { i } -2\widehat { j } +15\widehat { k } \)
  • D \(5\widehat { i } -10\widehat { j } +10\widehat { k } \)

Question - 4

 If |\(\vec { a } \)| = 4 and -3 ≤ λ ≤ 2 then the range of |λ\(\vec { a } \)| is

  • A [0, 8]
  • B [-12, 8]
  • C [0, 12]
  • D [8, 12]

Question - 5

If \(\vec { a } \) and \(\vec { b } \) are unit vectors, then what is the angle between \(\vec { a } \) and \(\vec { b } \) for \(\sqrt { 3 } \vec { a } -\vec { b } \) to be a unit vector?

  • A 30°
  • B 45°
  • C 60°
  • D 90°

Question - 6

If for non zero vectors \(\vec { a } \) and \(\vec { b } \), \(\vec { a } \) x \(\vec { b } \) is a unit vector and |\(\vec { a } \)| =  |\(\vec { b } \)| = \(\sqrt2\), then angle θ between vectors \(\vec { a } \) and \(\vec { b } \) is

  • A \(\frac { \pi }{ 2 } \)
  • B \(\frac { \pi }{ 3 } \)
  • C \(\frac { \pi }{ 6 } \)
  • D \(-\frac { \pi }{ 2 } \)

Question - 7

The area of a parrallelgram whose one diagonal is \(2\widehat { i } +\widehat { j } -2\widehat { k } \) and one side is \(3\widehat { i } +\widehat { j } -\widehat { k } \) is

  • A \(\widehat { i } -4\widehat { j } -\widehat { k } \)
  • B \(3\sqrt { 2 } \) sq unts
  • C \(6\sqrt { 2 } \) sq units
  • D 6 sq units

Question - 8

If \(\left| \vec { a } \right| =8,\) \(\left| \vec { b } \right| =3\) and \(\left| \vec { a.b } \right| =12\sqrt { 3 } \) then the value of \(\left| \vec { a } \times \vec { b } \right| \) is 

  • A 12
  • B \(12\sqrt { 3 } \)
  • C 6
  • D \(4\sqrt { 3 } \)

Question - 9

If vectors \(\widehat { i } +\widehat { j } +3\widehat { k } \), \(2\widehat { i } +\widehat { j } -\lambda \widehat { k } \), \(5\widehat { i } +2\widehat { j } +3\widehat { k } \) are coplanar, then value or λ is

  • A 4
  • B 0
  • C -3
  • D 2

Question - 10

In triangle ABC Fig which of the following is not true:

  • A \(\overrightarrow { AB } +\overrightarrow { BC } +\overrightarrow { CA } =\overrightarrow { 0 } \)
  • B \(\overrightarrow { AB } +\overrightarrow { BC } -\overrightarrow { AC } =\overrightarrow { 0 } \)
  • C \(\overrightarrow { AB } +\overrightarrow { BC } -\overrightarrow { AC } =\overrightarrow { 0 } \)
  • D \(\overrightarrow { AB } -\overrightarrow { CB } +\overrightarrow { CA } =\overrightarrow { 0 } \)
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