#### 12th Standard Maths Applications of Vector Algebra English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

Reg.No. :
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Maths

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

10 x 1 = 10
1. If $\vec{a}$ and $\vec{b}$ are parallel vectors, then $[\vec { a } ,\vec { c } ,\vec { b } ]$ is equal to

(a)

2

(b)

-1

(c)

1

(d)

0

2. If $\vec { a }$ and $\vec { b }$ are unit vectors such that $[\vec { a } ,\vec { b },\vec { a } \times \vec { b } ]=\frac { \pi }{ 4 }$, then the angle between $\vec { a }$ and $\vec { b }$ is

(a)

$\frac { \pi }{ 6 }$

(b)

$\frac { \pi }{ 4 }$

(c)

$\frac { \pi }{ 3 }$

(d)

$\frac { \pi }{ 2 }$

3. If the volume of the parallelepiped with $\vec { a } \times \vec { b } ,\vec { b } \times \vec { c } ,\vec { c } \times \vec { a }$  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with $(\vec { a } \times \vec { b } )\times (\vec { b } \times \vec { c } ),(\vec { b } \times \vec { c } )\times (\vec { c } \times \vec { a } )$ and $(\vec { c } \times \vec { a } )\times (\vec { a } \times \vec { b } )$as coterminous edges is,

(a)

8 cubic units

(b)

512 cubic units

(c)

64 cubic units

(d)

24 cubic units

4. If $\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c }$ where $\vec { a } ,\vec { b } ,\vec { c }$ are any three vectors such that $\vec { a } ,\vec { b }$ $\neq$ 0 and  $\vec { a } .\vec { b }$ $\neq$ 0 then $\vec { a }$ and $\vec { c }$ are

(a)

perpendicular

(b)

parallel

(c)

inclined at an angle $\frac{\pi}{3}$

(d)

inclined at an angle  $\frac{\pi}{6}$

5. The angle between the line $\vec { r } =(\hat { i } +2\hat { j } -3\hat { k } )+t(2\hat { i } +\hat { j } -2\hat { k } )$ and the plane $\vec { r } .(\hat { i } +\hat { j } )+4=0$ is

(a)

(b)

30°

(c)

45°

(d)

90°

6. The vector equation $\vec { r } =(\hat { i } -2\hat { j } -\hat { k } )+t(6\hat { i } -\hat { k) }$ represents a straight line passing through the points

(a)

(0,6,1)− and (1,2,1)

(b)

(0,6,-1) and (1,4,2)

(c)

(1,-2,-1) and (1,4,-2)

(d)

(1,-2,-1) and (0,-6,1)

7. The vector, d$\overset { \wedge }{ i } +\overset { \wedge }{ j } +2\overset { \wedge }{ k } ,\overset { \wedge }{ i } +\lambda \overset { \wedge }{ j } -\overset { \wedge }{ k }$ t and $2\overset { \wedge }{ i } -\overset { \wedge }{ j } +\lambda \overset { \wedge }{ k }$ are co-planar if

(a)

λ = -2

(b)

λ = 1+$\sqrt { 3 }$

(c)

λ = 1 - $\sqrt { 3 }$

(d)

λ = -2,1土 $\sqrt { 3 }$

8. 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$\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b }$

9. 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, $\frac { 1 }{ 2 }$)

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

(a)

4

(b)

$2\sqrt { 3 }$

(c)

$4\sqrt { 3 }$

(d)

$5\sqrt { 3 }$