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Byju's Answer
Standard XII
Mathematics
Definition of Vector
Determine the...
Question
Determine the angle which the vector
A
=
5
i
+
6
j
+
5
k
makes with
x
,
y
,
z
axis.
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Solution
Unit vector along X axis =
^
i
Unit vector along Y axis =
^
j
Unit vector along Z axis =
^
k
We use dot product to find angle
→
a
.
→
b
=
a
b
cos
θ
Now with X axis:
→
A
.
^
i
=
A
×
1
×
cos
θ
(
5
^
i
+
0
^
j
+
5
^
k
)
.
^
i
=
5
√
2
cos
θ
5
=
5
√
2
cos
θ
∴
cos
θ
=
1
√
2
θ
=
π
4
Now with Y axis:
→
A
.
^
j
=
A
×
1
×
cos
θ
(
5
^
i
+
0
^
j
+
5
^
k
)
.
^
j
=
5
√
2
cos
θ
0
=
5
√
2
cos
θ
∴
cos
θ
=
0
θ
=
π
2
Now with Z axis:
→
A
.
^
k
=
A
×
1
×
cos
θ
(
5
^
i
+
0
^
j
+
5
^
k
)
.
^
k
=
5
√
2
cos
θ
5
=
5
√
2
cos
θ
∴
cos
θ
=
1
√
2
θ
=
π
4
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