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Q.

The x-component of the resultant of several vectorsa) is equal to the sum of the x-components of the vectorsb) may be smaller than the sum of the magnitudes of the vectorsc) may be greater than the sum of the magnitudes of the vectorsd) 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

Sum of vectors a⇀,b⇀and c⇀is R⇀as shown in the figure.Magnitude of x-component of R =OMMagnitudfe of x-Component of  a⇀= OKMagnitude of x-Component of b⇀=  KLMagnitude of x-Component of C⇀= LMNow OM = OK + KL+LMAlso , OK < OA , KL < AB and BC > LMSo option - (2 ) is right
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The x-component of the resultant of several vectorsa) is equal to the sum of the x-components of the vectorsb) may be smaller than the sum of the magnitudes of the vectorsc) may be greater than the sum of the magnitudes of the vectorsd) may be equal to the sum of the magitudes of the vectors