Question:
If a unit vector is represented by $ 0.5 \widehat{ i} - 0 . 8 \widehat{j} + c \widehat{k}$ then the value of c is
If a unit vector is represented by $ 0.5 \widehat{ i} - 0 . 8 \widehat{j} + c \widehat{k}$ then the value of c is
Updated On: Sep 20, 2024
- $ \sqrt{ 0 . 0 1}$
- $ \sqrt{ 0 . 11}$
- 1
- $ \sqrt{ 0 . 39}$
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The Correct Option is B
Solution and Explanation
For a unit vector $ \hat{n}$, $| \hat{n} | = 1 $
$|0.5 \hat{i} - 0.8 \widehat{j} + c \hat{k} |^2 = 1^2 \Rightarrow 0.25 + 0 .64 + c^2 = 1 $
or c = $ \sqrt{ 0.11}$
$|0.5 \hat{i} - 0.8 \widehat{j} + c \hat{k} |^2 = 1^2 \Rightarrow 0.25 + 0 .64 + c^2 = 1 $
or c = $ \sqrt{ 0.11}$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration