Find the sine of the angle between the vectors
A = 3 - 4ſ + 5 k and B =
B =î - j + k.
(Ans. 1/5)
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Explanation:
Angle between vectors
a
,
b
be
then cosθ=
∣
∣
∣
∣
a
∣
∣
∣
∣
∣
∣
∣
∣
b
∣
∣
∣
∣
a
.
b
cosθ=
∣
∣
∣
∣
i
^
+2
j
^
+2
k
^
∣
∣
∣
∣
∣
∣
∣
∣
3
i
^
+2
j
^
+6
k
^
∣
∣
∣
∣
(
i
^
+2
j
^
+2
k
^
)(3
i
^
+2
j
^
+6
k
^
)
=
9
.
49
3+4+12
=
21
19
sinθ=
1−cos
2
θ
=
1−
21
2
19
2
=
21
21
2
−19
2
=
21
4
5
Also sinθ=
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
a
∣
∣
∣
∣
∣
∣
∣
∣
b
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
∣
∣
∣
∣
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