Suppose we have vectors as $$\vec{V} = 2\hat{i} + \hat{j} -\hat{k} $$ and

$$\vec{W} = \hat{i} + 3\hat{k} $$

So what will maximum value of $$k=[ \vec{U} \vec{V} \vec{W}]$$ for some unit vector $\vec{U}$ ?

I just came up with $$ \vec{V} \times\vec{W}$$ which is equal to $ 3\hat{i} -7 \hat{j} -\hat{k}$ . Now to maximse I took dot product in a way that it all add up by supposing vector $\vec{U} = \frac{\hat{i} - \hat{j} -\hat{k}}{\sqrt{3}} $ but came with wrong answer so how to do it?


After thinking a bit I realized that dot product can be maximum only if both the vectors are same so dot product with $\vec{V} \times \vec{W}$ and its unit vector maximized scalar triple product.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.