# JEE Main

Explore popular questions from Vectors for JEE Main. This collection covers Vectors previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Vectors

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Q 1. If {tex} | \vec { a } | = 4 , | \vec { b } | = 2 {/tex} and the angle between {tex} \vec { a } {/tex} and {tex} \vec { b } {/tex} is {tex} \frac { \pi } { 6 } {/tex} then {tex} ( \vec { a } \times \vec { b } ) ^ { 2 } {/tex} is equal to

A

48

16

C

{tex} \vec { a } {/tex}

D

none of these

##### Explanation

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Q 2. If {tex} \vec { a } , \vec { b } , \vec { c } {/tex} are vectors such that {tex} [ \vec { a } \quad \vec { b } \quad \vec { c } ] = 4 {/tex}
then {tex} \left[ \begin{array} { l l l } { \vec { a } \times \vec { b } } & { \vec { b } \times \vec { c } } & { \vec { c } \times \vec { a } } \end{array} \right] = {/tex}

16

B

64

C

4

D

8

##### Explanation

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Q 3. {tex} 3 \lambda \vec { c } + 2 \mu ( \vec { a } \times \vec { b } ) = 0 {/tex} then

A

{tex} 3 \lambda + 2 \mu = 0 {/tex}

{tex} 3 \lambda = 2 \mu {/tex}

C

{tex} \lambda = \mu {/tex}

D

{tex} \lambda + \mu = 0 {/tex}

##### Explanation

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Q 4. Consider {tex} A , B , C {/tex} and {tex} D {/tex} with position vectors {tex} 7 \hat { i } - 4 \hat { j } + 7 \hat { k } , \quad \hat { i } - 6 \hat { j } + 10 \hat { k } , \quad - \hat { i } - 3 \hat { j } + 4 \hat { k } \quad {/tex} and {tex} 5 \hat { i } - \hat { j } + 5 \hat { k } {/tex} respectively. Then {tex} A B C D {/tex} is a

A

rhombus

B

rectangle

C

parallelogram but not a rhombus

None of these

##### Explanation

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Q 5. If {tex} \vec { u } , \vec { v } {/tex} and {tex} \vec { w } {/tex} are three non-coplanar vectors, then {tex} ( \vec { u } + \vec { v } - \vec { w } ) \cdot ( \vec { u } - \vec { v } ) \times ( \vec { v } - \vec { w } ) {/tex} equals

{tex} \vec { u } \cdot (\vec { v } \times \vec { w } ){/tex}

B

{tex} \vec { u } \cdot \vec { w } \times \vec { v } {/tex}

C

{tex} 3 u \cdot \vec { u } \times \vec { w } {/tex}

D

0

##### Explanation

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Q 6. The vectors {tex} \overrightarrow { A B } = 3 \hat { i } + 4 \hat { k } {/tex} and {tex} \overrightarrow { A C } = 5 \hat { i } - 2 \hat { j } + 4 \hat { k } {/tex} are the sides of a triangle {tex} A B C {/tex}. The length of the median through {tex} A {/tex} is

A

{tex} \sqrt { 72 } {/tex}

{tex} \sqrt { 33 } {/tex}

C

{tex} \sqrt { 288 } {/tex}

D

{tex} \sqrt { 18 } {/tex}

##### Explanation

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Q 7. {tex} \vec { a } , \vec { b } , \vec { c } {/tex} are three vectors, such that {tex} \vec { a } + \vec { b } + \vec { c } = 0 , {/tex} where {tex} | \vec { a } | = 1 , \ | \vec { b } | = 2 , | \vec { c } | = 3 , \quad {/tex} then {tex} \quad \vec { a } \cdot \vec { b } + \vec { b } \cdot \vec { c } + \vec { c } \cdot \vec { a } \quad {/tex} is equal to

-7

B

7

C

1

D

0

##### Explanation

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Q 8. Let {tex} \vec { a } , \vec { b } {/tex} and {tex} \vec { c } {/tex} be three non-zero vectors such that no two of these are collinear. If the vector {tex} \vec { a } + 2 \vec { b } {/tex} is collinear with {tex} \vec { c } {/tex} and {tex} \vec { b } + 3 \vec { c } {/tex} is collinear with {tex} \vec { a } {/tex} ( {tex}\lambda {/tex} being some non-zero scalar) then {tex} \vec { a } + 2 \vec { b } + 6 \vec { c } {/tex} equals

A

{tex} \lambda \vec { c } {/tex}

B

{tex} \lambda \vec { b } {/tex}

C

{tex} \lambda \vec { a } {/tex}

0

##### Explanation

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Q 9. A particle is acted upon by constant forces {tex} 4 \hat { i } + \hat { j } - 3 \hat { k } {/tex} and {tex} 3 \hat { i } + \hat { j } - \hat { k } {/tex} which displace it from a point {tex} \hat { i } + 2 \hat { j } + 3 \hat { k } {/tex} to the point {tex} 5 \hat { i } + 4 \hat { j } + \hat { k } {/tex}. The work done in standard units by the forces is given by

A

25

B

30

40

D

15

##### Explanation

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Q 10. If {tex} \vec { a } , \vec { b } , \vec { c } {/tex} are non-coplanar vectors and {tex} \lambda {/tex} is a real number, then the vectors {tex} \vec { a } + 2 \vec { b } + 3 \vec { c } , \lambda \vec { b } + 4 \vec { c } {/tex} and {tex} ( 2 \lambda - 1 ) \vec { c } {/tex} are non-coplanar for

all except two values of {tex} \lambda {/tex}

B

all except one value of {tex} \lambda {/tex}

C

all values of {tex} \lambda {/tex}

D

no value of {tex} \lambda {/tex}

##### Explanation

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Q 11. Let {tex} \vec { a } , \vec { b } {/tex} and {tex} \vec { c } {/tex} be non-zero vectors such that {tex} ( \vec { a } \times \vec { b } ) \times \vec { c } = \frac { 1 } { 3 } | \vec { b } | | \vec { c } | \vec { a }{/tex} . If {tex} \theta {/tex} is the acute angle between the vectors {tex} b {/tex} and {tex} \vec { c } , {/tex} then {tex} \sin \theta {/tex} equals

A

{tex} \frac { 2 } { 3 } {/tex}

B

{tex} \frac { \sqrt { 2 } } { 3 } {/tex}

C

{tex} \frac { 1 } { 3 } {/tex}

{tex} \frac { 2 \sqrt { 2 } } { 3 } {/tex}

##### Explanation

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Q 12. If {tex} C {/tex} is the mid point of {tex} A B {/tex} and {tex} P {/tex} is any point outside {tex} A B , {/tex} then

A

{tex} \overrightarrow { P A } + \overrightarrow { P B } + \overrightarrow { P C } = 0 {/tex}

B

{tex} \overrightarrow { P A } + \overrightarrow { P B } + 2 \overrightarrow { P C } = \overrightarrow { 0 } {/tex}

C

{tex} \overrightarrow { P A } + \overrightarrow { P B } = \overrightarrow { P C } {/tex}

{tex} \overrightarrow { P A } + \overrightarrow { P B } = 2 \overrightarrow { P C } {/tex}