Question

Let v = 8j and let u be a vector with length 9 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u × v.

Answer 1

Answer:

$|u\times v|_{min}=0$

$|u\times v|_{max}=72$

Step-by-step explanation:

We are given that

v=8 j

|u|=9

Let u=ai+bj

We have to find the maximum and minimum values of the length of the vector

u × v.

$u\times v=\begin{vmatrix}i&j&k\\a&b&0\\0&8&0\end{vmatrix}=8ak$

$|u\times v|=\sqrt{(8a)^2}=\sqrt{64a^2}$

$|u|=\sqrt{a^2+b^2}=9$

$a^2+b^2=81$

The minimum value of $a^2$=0

Then, $|u\times v|_{min}=0$

Maximum value of  $a^2$=81

$|u\times v|_{max}=\sqrt{64(81)}=72$