Vector A points N-E and its magnitude is 3 kg/ms it is multiplied by the scalar λ such that λ = -4 second. Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity or not? (Irrelevant answers will be reported)
Answers
Explanation:
A=3kgm/r NE
A(-4)= -12 kg mr/r
magnitude= -12 kg.m
Correct Question: Vector A points N-E and its magnitude is 3 kg m/s. It is multiplied by the scalar λ such that λ = -4 second. Find the direction and magnitude of the new vector quantity. Does it represent the same physical quantity or not?
Answer: The new direction of vector would be southwest (S-W). The new magnitude would be equal to 12 kg m. The vector does not represent the same physical quantity.
Given:
The original direction of Vector A: North-east direction
The original magnitude of Vector A = 3 kg m/s.
To Find:
The new magnitude and direction of Vector A.
Solution:
→ We cannot add or subtract a vector and a scalar. We can only add or subtract a vector from another vector. Although we can multiply a given vector with a scalar quantity.
→ On multiplying a vector with a scalar, the resultant is still a vector.
→ On multiplying a vector with a scalar, its magnitude, direction or both might get changed.
→ On multiplying a vector with a negative scalar the direction of the vector gets reversed. The direction becomes just the opposite of the original direction of the vector.
→ On multiplying a given vector with a scalar 'λ', its magnitude also increases |λ| times.
→ Therefore on multiplying the vector A with λ = -4 second:
(1.) Its magnitude increases by 4 times and becomes equal to 12 kg m.
(2.) As 'λ' is negative, therefore its direction gets reversed. Hence the new direction of Vector A would be southwest (just opposite of Northeast).
(3.) It will now represent a new physical quantity with unit kg m.
Therefore the new direction of vector would be southwest (S-W). The new magnitude would be equal to 12 kg m. The vector does not represent the same physical quantity.
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