# NEET Physics Mathematical Tools Questions Solved

(1)

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Using sin rule, and taking case where

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(2)

Let angle betwee A & B is $\mathrm{\theta }$

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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

(2) $A+B=18$ …(i)

$12=\sqrt{{A}^{2}+{B}^{2}+2AB\mathrm{cos}\theta }$ …(ii)

$\mathrm{tan}\alpha =\frac{B\mathrm{sin}\theta }{A+B\mathrm{cos}\theta }=\mathrm{tan}90°$

$\mathrm{cos}\theta =-\frac{A}{B}$ …(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°

(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  have the directions indicated in the figure.Which of the following statements may be true?

(a) $\stackrel{\to }{b}+\stackrel{\to }{c}=\stackrel{\to }{-f}$                        (b) $\stackrel{\to }{d}+\stackrel{\to }{c}=\stackrel{\to }{f}$

(c) $\stackrel{\to }{d}+\stackrel{\to }{e}=\stackrel{\to }{f}$                        (d) $\stackrel{\to }{b}+\stackrel{\to }{e}=\stackrel{\to }{f}$

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

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In the given figure

(A)  Angle between $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ is $110°$

(B)  Angle between $\stackrel{\to }{\mathrm{C}}$ and $\stackrel{\to }{\mathrm{D}}$ is $60°$

(C)  Angle between $\stackrel{\to }{\mathrm{B}}$ and $\stackrel{\to }{\mathrm{C}}$ is $110°$

(D)  Angle between $\stackrel{\to }{\mathrm{B}}$ and $\stackrel{\to }{\mathrm{C}}$ is $70°$

(C)

Angle between vectors is angle between tails/heads.

For vector ,

we can translate vector

Now tails are joined

For vector ,

we can translate vector

Tails are joined

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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

(B)

For 2 vectors $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$,

Depending on $\mathrm{\theta }$, magnitude of resultant will lie between-

$\left|\mathrm{A}-\mathrm{B}\right|<\mathrm{R}<\mathrm{A}+\mathrm{B}$

In question,

$2\mathrm{N}<\mathrm{R}<14\mathrm{N}$

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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

(C)

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