Test: Addition & Subtraction of Vectors - Graphical Method (NCERT) - NEET

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