Arrange the vectors in descending order of their magnitudes.
(A) $\hat{i}+\hat{j}+\hat{k}$
(B) $2\hat{i}-3\hat{j}$
(C) $\frac{1}{2}\hat{i}-\frac{1}{3}\hat{j}$
(D) $2\hat{i}-\hat{k}$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
the correct answer is Option 2: (B), (D), (A), (C)
(a) Magnitude of a vector $\hat{i}+\hat{j}+\hat{k}$
= √{(1)2 + (1)2 + (1)2}
= √3
(b) Magnitude of a vector $2\hat{i}-3\hat{j}$ = √{(2)2 +(-3)2 }
= √13
(c) Magnitude of a vector $\frac{1}{2}\hat{i}-\frac{1}{3}\hat{j}$
= √{(1/2)2 +(-1/3)2 }
= (√13)/ 6
(d) Magnitude of vector $2\hat{i}-\hat{k}$ = √{(2)2 +(-1)2 }
= √5
√13 > √5 > √3 > √13⁄6
(B) > (D) > (A) > (C)