4.7 Given a + b + c + d = 0, which of the following statements are correct:
(a) a, b, c, and d must each be a null vector
(b) The magnitude of (a + c) equals the magnitude of (b + d)
(c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d
(d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
4.7 Given a + b + c + d = 0, which of the following statements are correct:
(a) a, b, c, and d must each be a null vector
(b) The magnitude of (a + c) equals the magnitude of (b + d)
(c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d
(d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
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1 Answer
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4.7
(a) This statement is In order to make a + b+ c + d = 0, it is not necessary to have all four given vectors to be null vectors.
(b) a + b + c +d = 0, ( a + c ) = - (b + d)Taking the magnitude of both LHS and RHS, | a + c| = | -(b + d)| = | b + d|
So the statement is True.
(c) Given a + b + c + d = 0, a = - (b + c + d)
Taking magnitude of both LHS and RHS, |a| = | -( b + c+ d)| = |b + c +d|
|a| ……….(1)
Equation (1) shows that the magnitude of a can never be greater than the sum of magnitudes of b,c and d. So the statement is True.
(d) In the given expression a + b + c + d = 0, the sum of 3 vectors
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Please find the solution below:
after 10 kicks,
v? = 3tî v? = 24cos 60°î + 24sin 60°? = 12î + 12√3?
v? = v? – v? = (12 – 3t)î + 12√3?
It is minimum when 12 - 3t = 0 ⇒ t = 4sec
ω = θ² + 2θ
α = (ωdω)/dθ = (θ² + 2θ) (2θ + 2)
At θ = 1rad.
ω = 3rad/s and α = 12rad/s²
a? = αR = 12 m/s² a? = ω²R = 9 m/s² A? = √ (a? ² + a? ²) = 15 m/s²
a? = v? ²/4r
a_A? = (v? ²/r²) × r = v? ²/r
a_A = 3v? ²/4r
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