4. Find the angle between the planes 7.(i + 3 – 2k) = 3
= 3 and 2x - 2y +z = 2.
Answers
Answered by
1
Step-by-step explanation:
Explanation:
To find the angle between two planes, one has to find the angle between normal vectors of these planes.
How to find a normal vector to a plane
Explanation of why the angle between two vectors, each one normal to a plane, gives the angle between the two involved planes
Normal Vectors
For the plane 1 ,
x
+
2
y
−
z
+
1
=
0
N
→
1
=
ˆ
i
+
2
⋅
ˆ
j
−
1
⋅
ˆ
k
For the plane 2 ,
x
−
y
+
3
z
+
4
=
0
N
→
2
=
ˆ
i
−
ˆ
j
+
3
⋅
ˆ
k
Angle between the 2 vectors
N
→
1
⋅
N
→
2
=
∣
∣
∣
N
→
1
∣
∣
∣
⋅
∣
∣
∣
N
→
2
∣
∣
∣
⋅
cos
α
=>
cos
α
=
N
→
1
⋅
N
→
2
∣
∣
∣
N
→
1
∣
∣
∣
⋅
∣
∣
∣
N
→
2
∣
∣
∣
N
→
1
⋅
N
→
2
=
1
⋅
1
+
2
⋅
(
−
1
)
+
(
−
1
)
(
3
)
=
1
−
2
−
3
=
−
4
∣
∣
∣
N
→
1
∣
∣
∣
=
√
1
2
+
2
2
+
(
−
1
)
2
=
√
1
+
4
+
1
=
√
6
∣
∣
∣
N
→
2
∣
∣
∣
=
√
1
2
+
(
−
1
)
2
+
3
2
=
√
1
+
1
+
9
=
√
11
cos
α
=
−
4
√
6
⋅
√
11
=>
cos
α
=
−
4
√
66
=>
α
=
119.50
∘
Answered by
1
thita equal to cos inverse -2/√14 or cos inverse - √2) √7
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