Three Dimensional Geometry Part 2

If

→

n1

is a vector normal to the plane determined by

^

i

and

^

i

+

^

j

then

→

n

1=|

^ i	^ j	^ k
1	0	0
1	1	0

|=

^

k

If

→

n

2 is a vector normal to the plane determined by

^

i

−

^

j

and

^

i

+

^

k

then
n2=|

^ i	^ j	^ k
1	−1	0
1	0	1

|=−

^

i

−

^

j

+

^

k

Vector

→

a

is parallel to

→

n

1×

→

n

2
i.e.

→

a

is parallel to |

^ i	^ j	^ k
0	0	1
−1	−1	1

|=

^

i

−

^

j

Given

→

b

=

^

i

−2

^

j

+2

^

k

Cosine of acute angle between

→

a

and

→

b

=|‌

→ a ⋅ → b

| → a |⋅| → b |

|=‌

1

√2

Obtuse angle between

→

a

and

→

b

=‌

3π

4