NEET Physics Mathematical Tools Questions Solved


Concept Videos :-

#23 | Vectors : Resolution 2D
#24 | Vectors: Resolution 3D

Concept Questions :-

Resolution of vectors

 

(1)

 

          

Vector A has 2 components,Component of A along B ,A =A.BBB2Component  to B=ASo,  A=A+A        A=A-A            = A-A.BBB2

Perpendicular component of A to B is= A-A.BBB2= 3i^+4j^-72i+j^= -i2+j2

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Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

Using sin rule, and taking case where α < β

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Concept Videos :-

#27 | Vectors: Multiplication with Vector : Cross Product 1
#28 | Vectors: Multiplication with Vector : Cross Product 2
#30 | Vectors: Triple Product
#31 | Vectors: Numericals

Concept Questions :-

Vector Product

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Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

(2)

Let angle betwee A & B is θ

   

R12=A2+B2+2ABcosθ tan90°=10=2BsinθA+2Bcosθ  A=-2Bcosθ  R12=4B2cos2θ+B2-4B2cos2θ  R1=B

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Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12 N. Then the magnitudes of the forces are 

(1) 12 N, 6 N

(2) 13 N, 5N

(3) 10 N, 8 N

(4) 16 N, 2 N

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

(2) A+B=18 …(i)

12=A2+B2+2ABcosθ …(ii)

tanα=BsinθA+Bcosθ=tan90°

cosθ=AB …(iii)

By solving (i), (ii) and (iii),

A = 13 N and B = 5 N

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NEET - 2016

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
(a)90° (b)45° (c) 180° (d) 0°

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors


(a) Suppose two vectors are P and Q. It is given that [P+Q]=[P-Q]

Let angle between P and Q is φ.
 P2+Q2+2PQ cosφ=P2+Q2-2PQcosφ
=> 4PQcosφ=0
=> cosφ=0   [P,Q≠0]
=> φ=π/2=90° 

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NEET - 2010

Six vector a through f have the directions indicated in the figure.Which of the following statements may be true?

(a) b+c=-f                        (b) d+c=f

(c) d+e=f                        (d) b+e=f

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

If two non-zero vectors are represented by the two adjust sides of a parallelogram, then the resultant is given by the diagonal of the parallelogram passing through the point of intersection of the two vectors 

            b+c=-f

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In the given figure

                           

(A)  Angle between A and B is 110°

(B)  Angle between C and D is 60°

(C)  Angle between B and C is 110°

(D)  Angle between B and C is 70°

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

 

(C)

                      

Angle between vectors is angle between tails/heads.

For vector A & B ,

we can translate vector A 

Now tails are joined  θ= 70°

For vector B & C ,

 we can translate vector B 

Tails are joined  θ= 110°

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A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

(A)  1 N

(B)  11 N

(C)  15 N

(D)  20 N

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

(B)   

 

For 2 vectors A and B,

                            

Depending on θ, magnitude of resultant will lie between-

                A-B<R<A+B

In question,

             8-6 <R<8+6

             2N<R<14N

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Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

(A)  2, 4, 8

(B)  4, 8, 16

(C)  1, 2, 1

(D)  0.5, 1, 2

Concept Videos :-

#20 | Vectors: Introduction
#21 | Vectors: Addition
#22 | Vectors : Subtraction

Concept Questions :-

Resultant of Vectors

(C)

Let there be 3 vectors A, B & C.Suppose magnitude of C is highest.For zero resultant,             C  A+BWhere A, B & C represents magnitude of A, B & CFor pair 1, 2, 1     C= 2     A= 1     B= 1Also,  2  1+1

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