Question

Vector Algebra

Answer 1

Show that the vector i+j+k is equally inclined to the axes OX, OY, and OZ.

Answer 2

ox is i
oy is j
oz is k
we'll find the unit vector of i+j+k
which is (i+j+k)/root 3
so the direction cosine is 1/root 3
wihch is the angles between the vector and three coordinate axes
which is same arccosine(1/root 3)= 60 degrees

Answer 3

call this vector i+j+k=a
define a unit vector on each axis:
OX=i, OY=j, and OZ=k
Now use the dot product:
\[\overrightarrow{a}\cdot\overrightarrow{OX}=||\overrightarrow{a}||*||\overrightarrow{OX}||\cos \theta\]so this can be solved for theta.
So use the dot product in the same way as is illustrated above for a dot OY and a dot OZ and you will see all angles come out the same.

Answer 4

:) ThankYou~