Question:
The value of P so that the vectors $2 \hat i - \hat j + \hat k, \hat i + 2 \hat j - 3 \hat k$ and $3 \hat i + P \hat j + 5 \hat k$ are coplanar should be
The value of P so that the vectors $2 \hat i - \hat j + \hat k, \hat i + 2 \hat j - 3 \hat k$ and $3 \hat i + P \hat j + 5 \hat k$ are coplanar should be
Updated On: Jul 7, 2022
- 16
- -4
- 4
- -8
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The Correct Option is B
Solution and Explanation
For coplanarity
$35mm \begin{vmatrix}
2 & -1 & 1\\
1 & 2 & -3\\
3 & P & 5\\
\end{vmatrix} = 0$
or $ 2(10 + 3P) + 1(5 + 9) +1(P - 6)=0$
or $ 20 + 6P + 5 + 9 + P - 6 = 0$
or $ 7P + 34 - 6 = 0$
or $ 7P + 28 = 0$
or $ 7P = -28$
$\Rightarrow P = - \frac{28}{7} = -4$
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Notes on Motion in a plane
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