If - - -k- - -k- and 2- -3- -mk- are coplanar- then find m-

Let a̅ =î +ĵ +k̂ , b̅ =î ĵ +k̂ c̅ =2î +3ĵ +mk̂ since a̅,b̅,c̅ are coplaner, so [a̅ b̅ c̅]=0 ] 1 amp; 1 amp; 1 1 amp; ...

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Standard XII

Mathematics

Condition for Coplanarity of Four Points

If î +ĵ +k̂...

Question

If $^i +^j +^k,^i -^j +^k$ and $2^i + 3^j + m^k$ are coplanar, then find $m$ .

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Solution

Let $¯ a =^i +^j +^k, ¯ b =^i -^j +^k ¯ c = 2^i + 3^j + m^k$

since $¯ a, ¯ b, ¯ c$ are coplaner, so $[¯ a ¯ b ¯ c] = 0$ ]\\$

$\begin{matrix} 1 & 1 & 1 1 & - 1 & 1 2 & 3 & m \end{matrix} = 0$
$1 (- m - 3) - 1 (m - 2) + 1 (3 + 2) = 0 m = 2$

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If ^i+^j+^k,^i−^j+^k and 2^i+3^j+m^k are coplanar, then find m.

Let¯a=^i+^j+^k,¯b=^i−^j+^k¯c=2^i+3^j+m^ksince ¯a,¯b,¯c are coplaner, so[¯a¯b¯c]=0]\\$1111−1123m=01(−m−3)−1(m−2)+1(3+2)=0m=2

If $^i +^j +^k,^i -^j +^k$ and $2^i + 3^j + m^k$ are coplanar, then find $m$ .

Let $¯ a =^i +^j +^k, ¯ b =^i -^j +^k ¯ c = 2^i + 3^j + m^k$

since $¯ a, ¯ b, ¯ c$ are coplaner, so $[¯ a ¯ b ¯ c] = 0$ ]\\$

$\begin{matrix} 1 & 1 & 1 1 & - 1 & 1 2 & 3 & m \end{matrix} = 0$
$1 (- m - 3) - 1 (m - 2) + 1 (3 + 2) = 0 m = 2$