If vectors a = 2i - 16j + 5k and b = 3i + j + 2k,

Question

If \(\vec{a} = 2\hat{i} - 16\hat{j} + 5\hat{k}\)  and \(\vec{b} = 3\hat{i} + \hat{j} + 2\hat{k},\) then find a vector \(\vec{c}\), so that \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) represents the sides of a right angled triangle.

Answer 1

Given that

 \(\vec{a} = 2\hat{i} - 16\hat{j} + 5\hat{k}\) 

\(\vec{a}\) and \(\vec{b}\) are perpendicular to each other or abgle between tham = 90,

Now if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are sides of a triangle then relation among them will be

From the above \(\vec{a}\) ,\(\vec{b}\) and \(\vec{c}\) represents the sides of a right angled triangle.

Hence required vector \(\vec{c}\) = \(5\hat{i} - 15\hat{j} + 7\hat{k}\)