Vector Algebra — Class 12 Maths Solution

Let $\vec a = \hat i + \hat j + \hat k$ and $\vec b = 2\hat i + 2\hat j + 2\hat k$

Direction cosines of $\vec a$ are $< \cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }} >$

Direction cosines of $\vec b$ are $< \cfrac{2}{{\sqrt {12} }},\cfrac{2}{{\sqrt {12} }},\cfrac{2}{{\sqrt {12} }} >$

i.e., $< \cfrac{1}{{\sqrt 3 }},\cfrac{1}{{\sqrt 3 }}\cfrac{1}{{\sqrt 3 }} >$

Hence, $\vec a \ne \vec b$ but $\vec a$ and $\vec b$ have same direction.