If either `a=0,b=0`, then a.b=0. But the converse need not to be true . Justify your answer with an example.

Explanation

If `a=0=0hat(i)+0hat(j)+0hat(k)` and b is non-zero i.e., `b=x hat(i)+yhat(j)+zhat(k)`
`therefore a.b =(0hat(i)+0hat(j)+0hat(k))(xhat(i)+yhat(j)+zhat(k))=(0xx x)+(0 xx y)+(0xx z)=0`
So, if `a=0 or b=0`, then for same `a.b=0`
To prove that converseneed not to be we have to prove that for two non-zero vectors a and b, a.b can be zero.
Let `a=2hat(i)+4hat(k)+3hat(k) and b=3hat(i)+3hat(j)-6hat(k)`
Then, `a.b=2.3+4.3+3.(-6)=6+12-18=0`
We now observe that `|a|=sqrt(a^2+4^2+3^2)=sqrt(29) therefore a ne 0`.
`|b|=sqrt(3^2+3^2+(-6)^2)=sqrt(54)`.
`therefore b ne 0`.
Hence, the converse of the given statement need not be true.