Question

If a unit vector is represented by \[0.5\hat{i}+0.8\hat{j}+c\hat{k}\] then the value of $c$ is
A.$1$
B.$\sqrt{0.8}$
C.$\sqrt{0.11}$
D.$\sqrt{0.01}$

Answer 1

Hint: A vector quantity can be defined as the physical quantity which has both magnitude and direction. A unit vector is a vector which has a magnitude of one unit. An example of vector quantity is acceleration, displacement, linear momentum. Vector addition does not follow our simple rules of mathematics.

Complete answer:
The given unit vector is \[0.5\hat{i}+0.8\hat{j}+c\hat{k}\]
Since the magnitude of unit vector is always equal to one
\[\left| {\hat{A}} \right|=1\]
\[\sqrt{{{\left( 0.5 \right)}^{2}}+{{\left( 0.8 \right)}^{2}}+{{c}^{2}}}=1\]
\[\Rightarrow {{c}^{2}}=0.11\]
\[\Rightarrow c=\sqrt{0.11}\]

VSo the answer is option C.

Additional Information:
Following are the rules for vector addition.
Addition of vectors is commutative.
Vectors cannot be added algebraically. It can only be added geometrically.
Vector addition means finding the resultant of a number of vectors acting on a body.
The component vectors whose resultant is to be calculated are independent of each other. Each vector acts as if the other vectors were absent.
If any two unit vectors $\mathbf{\hat{a}}$ and $\mathbf{\hat{b}}$ must not be considered as equal unit vectors just because they have the same magnitude because direction in which the vectors are taken might be different therefore these unit vectors are different from each other. Therefore, to define a vector both magnitude and direction should be specified.

Note:
The characteristics of the vectors are as follows:
1.Vectors possess magnitude as well as the direction.
2.It does not obey the ordinary law of algebra.
3.The magnitude as well as the direction changes.
4.Polar vector can be defined as a type of vector having a fixed point of application. An example is the velocity vector.