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Question

Physics Question on Motion in a plane

The value of P so that the vectors 2i^j^+k^,i^+2j^3k^2 \hat i - \hat j + \hat k, \hat i + 2 \hat j - 3 \hat k and 3i^+Pj^+5k^3 \hat i + P \hat j + 5 \hat k are coplanar should be

A

16

B

-4

C

4

D

-8

Answer

-4

Explanation

Solution

For coplanarity 35mm211 123 3P5 =035mm \begin{vmatrix} 2 & -1 & 1\\\ 1 & 2 & -3\\\ 3 & P & 5\\\ \end{vmatrix} = 0 or 2(10+3P)+1(5+9)+1(P6)=0 2(10 + 3P) + 1(5 + 9) +1(P - 6)=0 or 20+6P+5+9+P6=0 20 + 6P + 5 + 9 + P - 6 = 0 or 7P+346=0 7P + 34 - 6 = 0 or 7P+28=0 7P + 28 = 0 or 7P=28 7P = -28 P=287=4\Rightarrow P = - \frac{28}{7} = -4