find the area of the parallelogram that has the vectors as adjacent sides
u = -2i + j + 5k
v = 4i - 3j - 3k
the answer options are
a. 11
b. squareroot 26
c. 86
d. 2 squareroot 86
e. 1
I found the area to be |u×v| = |12i+14j+2k|
can you help me to figure out which answer option it is?
+33653 Take the square root of the sum of the squared coefficients of i, j and k.
.
The area of the parallelogram is the magnitude of the vector that is formed, when taking the cross product of the two vectors that make up the parallelogram.
In other words, the area of the parallelogram is the length of the cross product vector.
That is a simple Pythagoras;
\(A=\sqrt{12^2+14^2+2^2}=\sqrt{144+196+4}=\sqrt{344}=\sqrt{4*86}=2\sqrt{86}\)
