What is # || < -3, -3, 0 > || #?

1 Answer

Answer:

#3sqrt2#

Explanation:

Anything enclosed in #<># denote a vector which has direction componential magnitudes (i.e. -3 units on the x axis, -3 units on the y-axis, and 0 units at the z-axis.)

Furthermore, anything enclosed in #norm(<>)# denotes the norm or the 'overall' magnitude of the vector brought about by its respective components.

For example, in 2D, #||<2,3>|| # is the magnitude brought about the magnitude in both the x and y axes. In this case, it follows the Pythagorean Theorem where the magnitude of the vector is #\sqrt(4+9)# and is consequently the norm. Its direction is #arctan(y/x)# in degrees.

In your case, a 3D vector, finding the norm is just analogous to the Pythagorean Theorem and that is, #magnitude=sqrt((x^2+y^2+z^2))# or also #sqrt(((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2))# for two given vectors of the same order.

So,
#norm(<-3,-3,0>)=\sqrt((-3)^2+(-3)^2+(0)^2)=3\sqrt2#