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Q.

The x-component of the resultant of several vectors
a) is equal to the sum of the x-components of the vectors
b) may be smaller than the sum of the magnitudes of the vectors
c) may be greater than the sum of the magnitudes of the vectors
d) may be equal to the sum of the magitudes of the vectors

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a

only a

b

a, b & d

c

a, b, & c

d

b & d

answer is B.

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Detailed Solution

Question Image

Sum of vectors $\overset{⇀}{a}$ , $\overset{⇀}{b}$ and $\overset{⇀}{c}$ is $\overset{⇀}{R}$

as shown in the figure.

Magnitude of x-component of R =OM

Magnitudfe of x-Component of

$\overset{⇀}{a}$ = OK

Magnitude of x-Component of

$\overset{⇀}{b}$ = KL

Magnitude of x-Component of

$\overset{⇀}{C}$ = LM

Now OM = OK + KL+LM

Also , OK < OA , KL < AB and BC > LM

So option - (2 ) is right

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The x-component of the resultant of several vectors a) is equal to the sum of the x-components of the vectors b) may be smaller than the sum of the magnitudes of the vectors c) may be greater than the sum of the magnitudes of the vectors d) may be equal to the sum of the magitudes of the vectors