find the magnitude of a vector is equal to 3 ICAP + 2 j cap - 6 k cap and a unit vector in the direction of a vector
Answers
Answer:
Given
a
−2
i
^
+3
j
^
+
k
^
=2
i
^
+3
j
^
+1
k
^
Magnitude of
a
−
2
2
+3
2
+1
2
∣
a
∣=
4+9+1
=
14
.
Unit vector in direction of
a
=
magnitudeof
a
1
×
a
a
=
14
1
[2
i
^
+3
j
^
+1
k
^
]
a
=
14
2
i
^
+
14
3
j
^
+
14
1
k
^
Thus, unit vector in direction of
a
14
2
i
^
+
14
3
j
^
+
14
1
k
^
.
solution
Given
a
−2
i
^
+3
j
^
+
k
^
=2
i
^
+3
j
^
+1
k
^
Magnitude of
a
−
2
2
+3
2
+1
2
∣
a
∣=
4+9+1
=
14
.
Unit vector in direction of
a
=
magnitudeof
a
1
×
a
a
=
14
1
[2
i
^
+3
j
^
+1
k
^
]
a
=
14
2
i
^
+
14
3
j
^
+
14
1
k
^
Thus, unit vector in direction of
a
14
2
i
^
+
14
3
j
^
+
14
1
k
^
.
solution
Given
a
−2
i
^
+3
j
^
+
k
^
=2
i
^
+3
j
^
+1
k
^
Magnitude of
a
−
2
2
+3
2
+1
2
∣
a
∣=
4+9+1
=
14
.
Unit vector in direction of
a
=
magnitudeof
a
1
×
a
a
=
14
1
[2
i
^
+3
j
^
+1
k
^
]
a
=
14
2
i
^
+
14
3
j
^
+
14
1
k
^
Thus, unit vector in direction of
a
14
2
i
^
+
14
3
j
^
+
14
1
k
^
.
solution
Explanation:
Answer:
The magnitude of a vector A=3i+2j-6k is 7 units and the unit vector in the direction of the vector is
Explanation:
- A vector is a physical quantity described by both magnitude and direction
- The component form of a vector is given by the formula
where are components along X, Y, Z axes
are unit vectors along X, Y, Z axes
- The magnitude of that vector can be calculated as
- The unit vector in the direction of the vector is
From the question, we have
the component force of the vector
as compared to the above equation
now the magnitude of the vector unit
the unit vector along the given vector is