Question

The following sets represent magnitudes of three vectors. Which set of
vectors can never give a zero vector on addition :-
(1) 3, 4, 5
(2) 2, 1,3
(3) 12, 10, 23
(4) 13, 5, 12

Answer 1

Given:

The following sets represent magnitudes of three vectors.

To find:

Which set of vectors can never give a zero vector on addition ?

Calculation:

I will tell you the quickest way to solve this type of questions , using simple logical reasoning.

We shall use the RULE of TRIANGLE CONSTRUCTION :

• For a triangle to be constructed sum of two sides have to be greater than the third side.

Now, according to TRIANGLE LAW OF VECTORS, three vectors can give a resultant zero only when they can form a triangle.

So, in the given options, all the options follow the rule of triangle construction except :

(2) 2 , 1 , 3 ........... (see below)

$1 + 3 > 2 \\ 2 + 3 > 1 \\ 1 + 2 = 3$

So, using these values a triangle can't be constructed and hence these vectors can never give zero resultant.

$\star$ Hope It Helps.

Answer 2

Answer:

by triangle law of vector