69 815
Assignments Done
99,5%
Successfully Done
In February 2019

# Answer to Question #2167 in Linear Algebra for biju

Question #2167
If u = 2i − 3j + k, v = i − 2k, w = ai + bj + ck form an orthogonal basis of R3 , find the
possible values of a, b and c.
Further, obtain the angles x = i − 3j− 3k makes with each of these vectors.
b) Find the direction cosines of the perpendicular from the origin to the plane
3r.(2i − 3j+ k) + 7 = 0.
Let&#039;s construct the system of equations for a,b,c. By the definition of the orthonormal basis:

The angles can be obtained in the following way:
$|\vec{x}| = \sqrt{1+9+9}= \sqrt{19} \hspace{6mm} |\vec{u}|=|\vec{v}|=|\vec{w}|=1 \\ angle[x u] = \arccos{(\vec{x}\cdot\vec{u})/|x|} = \arccos {\frac{8}{\sqrt{19}}}\\ angle[x v] = \arccos{(\vec{x}\cdot\vec{v})/|x|} = \arccos {-\frac{5}{\sqrt{19}}} \\ angle[x w] = \arccos{(\vec{x}\cdot\vec{w})/|x|} = \arccos {-\frac{18}{\sqrt{19}\sqrt{70}}} \\$
To obtain further solution submit your questions to our control panel and our experts will assist you.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!