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Mathematics
Problem
The vectors
A
B
‾
=
3
i
^
−
2
j
^
+
2
k
^
\overline{AB} = 3\hat{i} - 2\hat{j} + 2\hat{k}
A
B
=
3
i
^
−
2
j
^
+
2
k
^
and
B
C
‾
=
−
i
^
+
2
k
^
\overline{BC} = -\hat{i} + 2\hat{k}
B
C
=
−
i
^
+
2
k
^
are the adjacent sides of a parallelogram ABCD then the angle between the diagonals is (A)
cos
−
1
(
1
85
)
\cos^{-1}\left(\sqrt{\frac{1}{85}}\right)
cos
−
1
(
85
1
)
(B)
π
−
cos
−
1
(
49
85
)
\pi - \cos^{-1}\left(\sqrt{\frac{49}{85}}\right)
π
−
cos
−
1
(
85
49
)
(C)
cos
−
1
(
1
2
2
)
\cos^{-1}\left(\frac{1}{2\sqrt{2}}\right)
cos
−
1
(
2
2
1
)
(D)
cos
−
1
(
3
10
)
\cos^{-1}\left(\sqrt{\frac{3}{10}}\right)
cos
−
1
(
10
3
)
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