Question

Suppose that the area of a parallelogram with vertices (0, 0, 0), (1, 0, 0), (1, 9, a) and (2, 9, a) is sqrt*97
.

Suppose also that the third vertex, (1, 9, a), makes an obtuse angle with the positive z-axis.

What is the value of a ?

Answer 1

familiar wid cross product, right ?

Answer 2

you need to solve :

\[\langle 1,0,0 \rangle \times \langle 1,9,a \rangle = \sqrt{97}\]

Answer 3

no, havent had much practice in cross products

Answer 4

\(||\langle 1,0,0 \rangle \times \langle 1,9,a \rangle|| = \sqrt{97}\) *

Answer 5

cross product of two vectors is defined as :
\(\vec{A} \times \vec{B} = |\vec{A}||\vec{B}|\sin \theta \)