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12th Standard Maths English Medium - Applications of Vector Algebra 1 Mark Creative Question Paper and Answer Key 2022 - 2023 Study Materials Sep-02 , 2022

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12th Standard Maths English Medium - Applications of Vector Algebra 1 Mark Creative Question Paper and Answer Key 2022 - 2023

Applications of Vector Algebra 1 Mark Creative Question Paper With Answer Key

12th Standard

    Reg.No. :
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Maths

Time : 00:15:00 Hrs
Total Marks : 15

    Multiple Choice Question

    15 x 1 = 15

  1. If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then __________

    (a)

    \(\left| \overset { \rightarrow }{ d } \right| \)

    (b)

    \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)

    (c)

    \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ 0 } \)

    (d)

    a, b, c are coplanar

  2. If \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are two unit vectors, then the vectors \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) \) is parallel to the vector ___________

    (a)

    \(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

    (b)

    \(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

    (c)

    2\(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

    (d)

    2\(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

  3. The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) is ____________

    (a)

    4

    (b)

    2\(\sqrt { 3 } \)

    (c)

    4\(\sqrt { 3 } \)

    (d)

    5\(\sqrt { 3 } \)

  4. If \(\overset { \rightarrow }{ a } \), \(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \) are any three vectors, then \(\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) \) if and only if __________

    (a)

    \(\overset { \rightarrow }{ b } \), \(\overset { \rightarrow }{ c } \) are collinear

    (b)

    \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ c } \) are collinear

    (c)

    \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are collinear

    (d)

    none

  5. The volume of the parallelepiped whose sides are given by \(\overset { \rightarrow }{ OA } =2\overset { \wedge }{ i } -3\overset { \wedge }{ j } \), \(\overset { \rightarrow }{ OB } =\overset { \wedge }{ i } +\overset { \wedge }{ j } -\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ OC } =3\overset { \wedge }{ i } -\overset { \wedge }{ k } \) is _____________

    (a)

    \(\frac { 4 }{ 13 } \)

    (b)

    4

    (c)

    \(\frac { 2 }{ 7 } \)

    (d)

    \(\frac { 4 }{ 9 } \)

  6. If  \(\left| \overset { \rightarrow }{ a } \right| =\left| \overset { \rightarrow }{ b } \right| =1\)such that \(\overset { \rightarrow }{ a } +2\overset { \rightarrow }{ b } \) and \(5\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \) are perpendicular to each other, then the angle between \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) is _______________

    (a)

    45o

    (b)

    60o

    (c)

    cos-1 \(\left( \frac { 1 }{ 3 } \right) \)

    (d)

    cos-1 \(\left( \frac { 2 }{ 7 } \right) \)

  7. The angle between the vector \(3\overset { \wedge }{ i } +4\overset { \wedge }{ j } +\overset { \wedge }{ 5k } \) and the z-axis is ___________

    (a)

    30o

    (b)

    60o

    (c)

    45o

    (d)

    90o

  8. The p.v, OP of a point P make angles 60o and 45o with X and Y axis respectively. The angle of inclination of  \(\overset { \rightarrow }{ OP } \) with z-axis is ___________

    (a)

    75o

    (b)

    60o

    (c)

    45o

    (d)

    3

  9. If \(\overset { \rightarrow }{ a } =\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ 3k } \), \(\overset { \rightarrow }{ b } =-\overset { \wedge }{ i } +\overset { \wedge }{ 2j } +\overset { \wedge }{ k } \), \(\overset { \rightarrow }{ c } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } \) then \(\overset { \rightarrow }{ a } +\left( -\overset { \rightarrow }{ b } \right) \) will be perpendiculur to \(\overset { \rightarrow }{ c } \) only when t = _________________

    (a)

    5

    (b)

    4

    (c)

    3

    (d)

    \(\frac { 7 }{ 3 } \)

  10. If θ is the angle between the vectors \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow}{b} \), then sin θ is ___________ 

    (a)

    \(\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| } \)

    (b)

    \(\frac { \left| \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right| }{ \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } } \)

    (c)

    \(\sqrt { 1-{ \left( \frac { \overset { \rightarrow }{ a. } \overset { \rightarrow }{ b } }{ \left| \overset { \rightarrow }{ a } \right| \left| \overset { \rightarrow }{ b } \right| } \right) }^{ 2 } } \)

    (d)

    0

  11. If the vector \(\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ 2k } \), \(\overset { \wedge }{ -i } +\overset { \wedge }{ 2k } \) and \(2\overset { \wedge }{ i } +x\overset { \wedge }{ j } -y\overset { \wedge }{ k } \)  are mutually orthogonal, then the values of x, y, z are _________

    (a)

    (10, 4, 1)

    (b)

    (-10, 4, 1)

    (c)

    (-10, -4, \(\frac { 1 }{ 2 } \))

    (d)

    (-10, 4, \(\frac { 1 }{ 2 } \))

  12. If \(\overset { \rightarrow }{ a } =\left| \overset { \rightarrow }{ a } \right| \overset { \rightarrow }{ e } \) then \(\overset { \rightarrow }{ e } .\overset { \rightarrow }{ e } \) is _____________

    (a)

    0

    (b)

    e

    (c)

    1

    (d)

    \(\overset { \rightarrow }{ 0 } \)

  13. The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is _____________

    (a)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (b)

    4 \(\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \)

    (c)

    \(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

    (d)

    4 \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

  14. If \(\overset { \rightarrow }{ p } \times \overset { \rightarrow }{ q } =2\overset { \wedge }{ i } +3\overset { \wedge }{ j } \), \(\overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } =3\overset { \wedge }{ i } +2\overset { \wedge }{ k } \) then \(\overset { \rightarrow }{ p } .\left( \overset { \rightarrow }{ q } \left( \overset { \rightarrow }{ r } \times \overset { \rightarrow }{ s } \right) \right) \) is _____________

    (a)

    9

    (b)

    6

    (c)

    2

    (d)

    5

  15. If the work done by a force \(\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +m\overset { \wedge }{ j } -\overset { \wedge }{ k } \) in moving the point of application from(1, 1, 1) to (3, 3, 3) along a straight line is 12 units, then m is _____________

    (a)

    5

    (b)

    2

    (c)

    3

    (d)

    6

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