Find the value of a- if the vectors 2-k- -2-3k- and 3-a-5k- are coplanar-

We have, | 2 amp; 1 amp; 1 1 amp; 2 amp; 3 3 amp; a amp; 5 | =0 2( 10 + 3a) + ( 5 + 9) + ( a 6) = 0 20 + 6a + 1 ...

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Standard XII

Mathematics

Condition for Coplanarity of Four Points

Find the valu...

Question

Find the value of $\to a$ if the vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + a^j + 5^k$ are coplanar?

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Solution

We have,
$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & a & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$2 (10 + 3 a) + (5 + 9) + (a - 6) = 0$
$20 + 6 a + 14 + a - 6 = 0$
$7 a + 28 = 0$
$a = \frac{- 28}{7} = - 44$
Then,
We get $- 4$

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Find the value of →a if the vectors 2^i−^j+^k,^i+2^j−3^k and 3^i+a^j+5^k are coplanar?

We have,∣∣ ∣∣2−1112−33a5∣∣ ∣∣=02(10+3a)+(5+9)+(a−6)=020+6a+14+a−6=07a+28=0a=−287=−44Then,We get −4

Find the value of $\to a$ if the vectors $2^i -^j +^k,^i + 2^j - 3^k$ and $3^i + a^j + 5^k$ are coplanar?

We have,
$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & a & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$2 (10 + 3 a) + (5 + 9) + (a - 6) = 0$
$20 + 6 a + 14 + a - 6 = 0$
$7 a + 28 = 0$
$a = \frac{- 28}{7} = - 44$
Then,
We get $- 4$