Addition & Subtraction of Vectors - Graphical Method (NCERT) Free MCQ Practice

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 be zero in many ways other than each of a, b, c, and d being a null vector.
(b) Correct, as a + b + c + d = 0 implies a + c = -(b + d). Thus, the magnitude of (a + c) is equal to the magnitude of (b + d).
(c) Correct, since a + b + c + d = 0, so a = -(b + c + d). The magnitude of a is equal to the magnitude of (b + c + d). The sum of the magnitudes of b, c, and d will always be greater than or equal to the magnitude of a, so the statement is correct.
(d) Correct, because a + b + c + d = 0 means (b + c) + (a + d) = 0. The resultant sum of three vectors (b + c), a, and d can be zero only if (b + c) is in the plane of a and d. If a and d are collinear, then (b + c) must be along the line of a and d. Hence, the 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