8) i.j is equal to :
A) zero
B) one
C) square of magnitude
D) null vector
Answers
Explanation:
(a) In order to make vectors a + b + c + d = 0, it is not necessary to have all the four given vectors to be null vectors. There are many other combinations which can give the sum zero.
(b) Correct
a + b + c + d = 0
a + c = -(b + d)
Taking modulus on both the sides, we get:
| a + c | = | -(b + d)| = | b + d |
Hence, the magnitude of (a + c) is the same as the magnitude of (b + d).
(c) Correct
a + b + c + d = 0
a = - (b + c + d)
Taking modulus both sides, we get:
| a | = | b + c + d |
| a | ≤ | b | + | c | + |d| .... (i)
Equation (i) shows that the magnitude of a is equal to or less than the sum of the magnitudes of b, c, and d.
Hence, the magnitude of vector a can never be greater than the sum of the magnitudes of b, c, and d.
(d) Correct
For a + b + c + d = 0
a + (b + c) + d = 0
The resultant sum of the three vectors a, (b + c), and d can be zero only if (b + c) lie in a plane containing a and d, assuming that these three vectors are represented by the three sides of a triangle.
If a and d are collinear, then it implies that the vector (b + c) is in the line of a and d. This implication holds, only then the vector sum of all the vectors will be zero.
Answer:
B)one
Explanation: