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

12th Standard

Reg.No. :
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Maths

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

9 x 1 = 9
1. If a vector $\vec { \alpha }$ lies in the plane of $\vec { \beta }$ and $\vec { \gamma }$ , then

(a)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$ = 1

(b)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= -1

(c)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= 0

(d)

$[\vec { \alpha } ,\vec { \beta } ,\vec { \gamma } ]$= 2

2. If $\vec { a } ,\vec { b } ,\vec { c }$ are three non-coplanar vectors such that $\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } }$, then the angle between

(a)

$\frac { \pi }{ 2 }$

(b)

$\frac { 3\pi }{ 6 }$

(c)

$\frac { \pi }{ 4 }$

(d)

${ \pi }$

3. If the line $\frac { x-2 }{ 3 } =\frac { y-1 }{ -5 }= \frac { x+2 }{ 2 }$ lies in the plane x + 3y + - αz + β = 0, then (α, β) is

(a)

(-5, 5)

(b)

(-6, 7)

(c)

(5, 5)

(d)

(6, -7)

4. 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)

5. Let $\overset { \rightarrow }{ a }$,$\overset { \rightarrow }{ b }$ and $\overset { \rightarrow }{ c }$ be three non- coplanar vectors and let $\overset { \rightarrow }{ p } ,\overset { \rightarrow }{ q } ,\overset { \rightarrow }{ r }$ be the vectors defined by the relations $\overset { \rightarrow }{ P } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ q } =\frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ r } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] }$ Then the value of  $\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r }$=

(a)

0

(b)

1

(c)

2

(d)

3

6. 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)

$\frac { 4 }{ 9 }$

7. If $\left| \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right| =\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b }$then the angle between the vector $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ b }$ is _____________

(a)

$\frac { \pi }{ 4 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 6 }$

(d)

$\frac { \pi }{ 2 }$

8. If $\overset { \rightarrow }{ d }$ = $\lambda \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) +\mu \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\omega \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right)$ and ${ \left| \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right| }=\frac { 1 }{ 8 }$ then λ + μ + ω is _____________

(a)

0

(b)

1

(c)

8

(d)

8$\overset { \rightarrow }{ d } .\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right)$

9. Let $\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,$ and $\overset { \rightarrow }{ c }$ be three vectors having magnitudes 1, 1, 2 respectively.
If $\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } =0$ then the acute angle between $\overset { \rightarrow }{ a }$ and $\overset { \rightarrow }{ c }$ is ____________________

(a)

0

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 6 }$

(d)

$\frac { 2\pi }{ 3 }$