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12th Standard English Medium Maths Subject Applications of Vector Algebra Creative 2 Mark Questions with Solution Part - I

12th Standard

    Reg.No. :
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Maths

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

    2 Marks

    5 x 2 = 10
  1. A force of magnitude 6 units acting parallel to  displaces the point of application from (1, 2, 3) to (5, 3, 7). Find the work done.

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    b

  2. Forces 2\overset { \wedge }{ i } +7\overset { \wedge }{ j } 2\overset { \wedge }{ i } -5\overset { \wedge }{ j } +6\overset { \wedge }{ k } -\overset { \wedge }{ i } +2\overset { \wedge }{ j } -\overset { \wedge }{ k }  act at a point P whose position vector is 4\overset { \wedge }{ i } -3\overset { \wedge }{ j } -2\overset { \wedge }{ k } Find  the vector moment of the resultant of these forces acting at P about this point Q whose position vector is 6\overset { \wedge }{ i } +\overset { \wedge }{ j } -3\overset { \wedge }{ k }

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    3

  3. Find the parametric form of vector equation of a line passing through a point (2, -1, 3) and parallel to line { \overset { \rightarrow }{ r } }=\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) +t\left( 2\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \right)

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    p=-1

  4. If the planes { \overset { \rightarrow }{ r } }.\left( \overset { \wedge }{ i } +2\overset { \wedge }{ j } +3\overset { \wedge }{ k } \right) =7 and { \overset { \rightarrow }{ r } }.\left( \lambda \overset { \wedge }{ i } +2\overset { \wedge }{ j } -7\overset { \wedge }{ k } \right) =26 are perpendicular. Find the value of λ.

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    ∆=4

  5. Let \overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c }  be unit vectors such \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } =\overset { \rightarrow }{ a } .\overset { \rightarrow }{ c } =0 and the angle between \overset { \rightarrow }{ b }  and \overset { \rightarrow }{ c }  is \frac { \pi }{ 6 } Prove that \overset { \rightarrow }{ a } =\pm 2\left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right)

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    Type I even degree reciprocal equation

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