Q. 73.6( 33 Votes )

# Given a + b + c + d = 0, which of the following statements are correct:

A. a, b, c, and d must each be a null vector,

B. The magnitude of (a + c) equals the magnitude of (b + d),

C. The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d,

D. b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?

Answer :

A. Incorrect

Explanation: It is not necessary that the vectors ,, and be null vectors for their sum to be a null vector. There can be other combinations as well. For example, if then

.

B. Correct

Explanation:

⇒

Taking modulus on both sides,

⇒

Hence, magnitude of () is equal to the magnitude of ().

C. Correct

Explanation:

⇒

Taking modulus on both sides,

⇒

Hence, the magnitude of is always equal to the magnitude of and can never be greater than that.

D. Correct

Explanation: For the sum to be a null vector, the vectors , and must be three sides of a triangle according to triangle law of vector addition. The three sides of a triangle lie on the same plane. Hence, the vectors , and must be coplanar. But if and are collinear, then must lie on the same line and in opposite direction in order to cancel out in the sum .

NOTE: Triangle law of vector addition states that when two vectors are represented by two sides of a triangle in magnitude and direction taken in same order then third side of the third side of that triangle represents in magnitude and direction the resultant of the vectors.

Rate this question :

If |A|= 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II

If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A B and in column II.