1. can the directions of three vector of magnitude 300ft 400 ft and 700 ft be ar

Question

1. can the directions of three vector of magnitude 300ft 400 ft and 700 ft be arranged so as to be in equilibrum? Draw a vector diagram to verifty your answer

2. add two vectors in such a way that the magnitude of the resultant is smaller than the magnitude of either of the given vectors

3. exoress the resulation of the system in the above questions in terms of cosine law and state the conditions that must prevail when the magnitude of the resultant is a. equal to b. smaller than and c. larger than the diagnonal of a rectangular parallelogram

Explanation / Answer

Answer question

1) yes

the vectors 300*400 should be in one direction(+xaxis or +y axis) and the vector of magnitude should be in opposite direction (-xaxis or -y axis)


2) if 300&400 are perpendicular and 700 is opposite to the resultant of the 300*400.then

resultant of 300&400 = sqrt(300^2+400^2) = sqrt(250000)= 500

nert resultant = 700-500 = 200 which is smaller than either of the given vectors

3) R ^2 = a^2+b^2+2*a*b*cos(theta)

i) R = a .....cos(theta ) = -b/2a
ii)   R = b .....cos(theta ) = -a/2b


iii) R = a .....cos(theta ) = -b/2a

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