If u= j+4 k, v= i+3 k and w=, i+, j are vectors in 3-dimensional space, then the maximum p…

Question

If $\vec u=\hat j+4\hat k$, $\vec v=\hat i+3\hat k$ and $\vec w=\cos	heta\,\hat i+\sin	heta\,\hat j$ are vectors in 3-dimensional space, then the maximum possible value of $|(\vec u	imes\vec v)\cdot\vec w|$ is:

Accepted Answer

$$\vec u\times\vec v = \begin{vmatrix}\hat i&\hat j&\hat k\0&1&4\1&0&-3\end{vmatrix} = -3\hat i+4\hat j-\hat k$$

$$(\vec u\times\vec v)\cdot\vec w = -3\cos\theta+4\sin\theta$$

Maximum of $|{-3\cos\theta+4\sin\theta}|$ is $\sqrt{9+16}=5$.

Solutions · 1