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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

a , b , c are 3 non-coplanar unit vectors inclined at angle ( 2 ) to each other. If the volume of tetrahedron formed by these vectors is 1 360 , then find the value of 10 (3 ^2 -2 ^3 )

Correct answer

9

Step-by-step solution

Given, a b = b c = c a = Volume of tetrahedron = 1 6 [ array lll a & b & c array ] Now, [ array lll a & b & c array ]^2= | array ccc 1 & & & 1 & & & 1 array | aligned 36 V^2 & =(1+2 )(1- )^2 36 1 360 & =(1+2 )(1- )^2= 1 10 3 ^2 -2 ^3 & = 9 10 aligned

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