Test: Addition & Subtraction of Vectors (May 17) - JEE MCQ

Multiplying any vector by zero will result in a null vector.
So, the property of null vector is wrongly mention in option (C)
Hence, the correct option is (C).

(a) Incorrect, because a + b + c + d can zero in many ways other than that (vector a, b, c, and d) must each be a null vector.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.

Neither the magnitude of vectors nor the angle between the vectors is changed. So, magnitude of the resultant remains unchanged. However, the direction of the resultant will be changed.

Let sides OC, OG and OA represent x, y and z respectively.

Resultant of forces = 6i + √72 j + 6j = vector R

R = √(36 + 72 + 36) = √144 = 12 N

Resultant of OA and OC is along OB and of magnitude √72

(∵ they are perpendicular)

∴ Resultant of OC, OG and OA is same as OB √72 + OG √72

Its resultant will be along OE.

The velocity of the rain and the wind are represented by the vectors  as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity  If θ is the angle which resultant velocity  makes with the vertical, then

Radius of the circular path, r = 70m
Time takes to complete one round, t = 11s
Total length of the path, s = 2πr = 2*22/7*70 = 440m

Force, area and velocity all are a set of different or the same fundamental quantities multiplied or divided together while current itself is a fundamental quantity and can be expressed in terms of any other.

A projectile is the name given to any body which once thrown into space with some initial velocity, moves thereafter under the influence of gravity alone without being propelled by an engine or fuel. The path followed by a projectile is called its trajectory.

The vector product of two vectors depends upon the sine of the angle between the vectors and when the vectors are parallel the sine component would be zero hence the resultant is a null vector.