Question

write two different vectors having same magnitude

Answer 1

Toolbox:Two vectors can have same magnitude,if their lengths are equal.

Step 1:

Consider a vector a→=i^+j^+k^a→=i^+j^+k^ and b→=i^−j^−k^b→=i^−j^−k^.

Now let us compute the magnitude of a→a→

∣a→∣=12+12+12−−−−−−−−−−√∣a→∣=12+12+12

=3–√=3

Hence ∣a→∣=3–√∣a→∣=3

Step 2:

Next let us compute the magnitude of b→b→

∣b→∣=12+(−1)2+(−1)2−−−−−−−−−−−−−−−√∣b→∣=12+(−1)2+(−1)2

=12+12+12−−−−−−−−−−√=12+12+12

=3–√=3

Hence ∣b→∣=3–√∣b→∣=3

Step 3:

Therefore a→a→ and b→b→ are having same magnitude .

Hence a→=i^+j^+k^a→=i^+j^+k^ and b→=i^−j^−k^b→=i^−j^−k^ are two vectors which are equal in magnitude.

Answer 2

Two vectors are said to be equal if they have the same direction,but their magnitude can be different.