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11th Standard English Medium Maths Subject Vector Algebra - I Creative 2 Mark Questions with Solution Part - II

11th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 10

    2 Marks

    5 x 2 = 10
  1. Show that the vectors \(3\hat { i } -2\hat { j } +\hat { k } \) ,\(\hat { i } -3\hat { j } +5\hat { k } \) and \(2\hat { i } +\hat { j } -4\hat { k } \) form a right angled triangle.

  2. If \(\vec { a } ,\vec { b } \) are any two vectors, then prove that \(\left| \vec { a } \times \vec { b } \right| ^{ 2 }+\left( \vec { a } .\vec { b } \right) ^{ 2 }=\left| \vec { a } \right| ^{ 2 }\left| \vec { b } \right| ^{ 2 }\) 

  3. Find the angle between the vectors \(2\vec { i } +\vec { j } -\vec { k } \) and \(\vec { i } +2\vec { j } +\vec { k } \) by using cross product.

  4. If \(\vec { a } \times \vec { b } =\vec { c } \times \vec { d } \) and \(\vec { a } \times \vec { c } =\vec { b } \times \vec { d } \) show that \(\vec { a } -\vec { d } \) and \(\vec { b } -\vec { d } \)are parallel.

  5. If \(\left| \vec { a } \right| =2,\) ,\(\left| \vec { b } \right| =7\) and \(\vec { a } \times \vec { b } =3\hat { i } -2\hat { j } +6\hat { k } \) find the angle between \(\vec { a } \) and \(\vec { b } \)

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