The value of n so that vectors $2 \land i + 3 \land j - 2 \land k, 5 \land i + n \land j + \land k$ and $- \land i + 2 \land j + 3 \land k$ may be coplanar, will be :-

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Solution

The correct option is A 18
The given three vectors will be coplanar, if the determinant with the coefficients of the vectors is zero, i.e, $∣ ∣ ∣ ∣ \begin{matrix} 2 & 3 & - 2 5 & n & 1 - 1 & 2 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$
or $2 (3 n - 2) - 3 (15 + 1) + (- 2) (10 + n) = 0$
or $6 n - 4 - 48 - 20 - 2 n = 0$
or $4 n = 72$
or $n = 18$

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The value of n so that vectors 2∧i+3∧j−2∧k,5∧i+n∧j+∧k and −∧i+2∧j+3∧k may be coplanar, will be :-

The correct option is A 18The given three vectors will be coplanar, if the determinant with the coefficients of the vectors is zero, i.e, ∣∣ ∣∣23−25n1−123∣∣ ∣∣=0 or 2(3n−2)−3(15+1)+(−2)(10+n)=0or 6n−4−48−20−2n=0or 4n=72or n=18

The value of n so that vectors $2 \land i + 3 \land j - 2 \land k, 5 \land i + n \land j + \land k$ and $- \land i + 2 \land j + 3 \land k$ may be coplanar, will be :-