If vectors 2- - -k- - - -2- -3k- and 3- -a- -5k- are coplanar- then find the value of a-

The given three vectors will be co planar if #160; | [ 2 amp; 1 amp; 1; 1 amp; 2 amp; 3; 3 amp; a amp; 5 ]| =0 2( 10 ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

If vectors ...

Question

If vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + a^j + 5^k$ are coplanar, then find the value of $a$ .

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Solution

The given three vectors will be co-planar if
$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & a & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$2 (10 + 3 a) + 1 (5 + 9) + 1 (a - 6) = 0$
$\Rightarrow a = - 4$

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If vectors 2^i−^j+^k, ^i+2^j−3^k and 3^i+a^j+5^k are coplanar, then find the value of a.

The given three vectors will be co-planar if ∣∣ ∣∣2−1112−33a5∣∣ ∣∣=02(10+3a)+1(5+9)+1(a−6)=0⇒a=−4

If vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + a^j + 5^k$ are coplanar, then find the value of $a$ .

The given three vectors will be co-planar if
$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & a & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$2 (10 + 3 a) + 1 (5 + 9) + 1 (a - 6) = 0$
$\Rightarrow a = - 4$