Let be ( ) natural numbers in AP such that volume of parallelopiped formed by vectors

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

a_1, a_2, \dots, a_n

n

(

n \geq 10

) natural numbers in AP such that volume of parallelopiped formed by vectors

\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}

\vec{b} = a_2\hat{i} + a_3\hat{j} + a_1\hat{k}

and

\vec{c} = a_3\hat{i} + a_1\hat{j} + a_2\hat{k}

is 54 then

a_6

equals: (A) 2 (B) 5 (C) 7 (D) 10