Multiplying or dividing vectors by scalars results in a. vectors. b. scalars. c. vectors if multiplied or scalars if divided. d.
2 answers:
Let A = i+j+k be a vector and B = 3 be any scalar,
Multiplying A and B,
AB = (i+j+k)3 = 3i+3j+3k
Which is a new vector whose direction is same as the old but it's 3 times greater in length than the old vector(i+j+k).
Now, dividing A and B,
A/B = (i+j+k)/3 =
Which is again a new vector whose direction is same as the old but now it's 1/3 times small in length than the old vector.
Direction is same because we multiplied by positive scalar. If we multiply A by suppose -1, -4, -1000000 or any negative number, it's direction will reverse.
Thus, if we multiply a vector with scalar, it's length increases. If we divide, it shrinks.
Multiplying A and B,
AB = (i+j+k)3 = 3i+3j+3k
Which is a new vector whose direction is same as the old but it's 3 times greater in length than the old vector(i+j+k).
Now, dividing A and B,
A/B = (i+j+k)/3 =
Which is again a new vector whose direction is same as the old but now it's 1/3 times small in length than the old vector.
Direction is same because we multiplied by positive scalar. If we multiply A by suppose -1, -4, -1000000 or any negative number, it's direction will reverse.
Thus, if we multiply a vector with scalar, it's length increases. If we divide, it shrinks.
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Answer:
Explanation:
A charge located at a point will experience a zero electrostatic force if the resultant electric field on it due to any other charge(s) is zero.
is located at the origin. The net force on it will only be zero if the resultant electric field intensity due to
and
at the origin is equal to zero. Therefore we can perform this solution without necessarily needing the value of
.
Let the electric field intensity due to be +
and that due to
be -
since the charge is negative. Hence at the origin;
From equation (1) above, we obtain the following;
From Coulomb's law the following relationship holds;
where is the distance of
from the origin,
is the distance of
from the origin and k is the electrostatic constant.
It therefore means that from equation (2) we can write the following;
k can cancel out from both side of equation (3), so that we finally obtain the following;
Given;
Substituting these values into equation (4); we obtain the following;
It is the acceleration of an object in free fall
Explanation:
When an object is in free fall, it is subjected only to one force: the force of gravity, which pulls the object downward, with a magnitude (near the Earth's surface) which is given by
where
m is the mass of the object
is the acceleration due to gravity
We can apply Newton's second law to the object in free fall:
where
F is the net force on the object
a is the acceleration of the object
m is the mass
However, since there is only the force of gravity acting on the object, the net force is equal to the force of gravity: so we can equate the two equations, obtaining that
Which means that the acceleration of an object in free fall (acted upon the force of gravity only) is equal to the acceleration due to gravity, .
Learn more about gravity:
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