Find the value of 'p' for which p( i + j + k ) is a unit vector-

p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) is a unit vector if |p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) |= 1

Now, |p(\(\hat{i}\)+\(\hat{j}\)+ \(\hat{k}\)) |= 1

⇒ √(p²+p²+p²)= 1

⇒ √(3p²)= 1

⇒ √(3)p= 1

⇒  p= ±1/√3