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Question

The volume of the tetrahedron formed 4^i+5^j+^k,^j+^k,3^i+9^j+4^k,4(^i+^j+^k) is:

A
7
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B
9
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C
11
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D
13
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Solution

The correct option is C 11
a=4^i+5^j+^k
b=(1)^j+^k
c=3^i+9^j+4^k
d=(4)^i+4^j+4^k
Let us take the tetrahedral to be originating from the origin.
ie, the three vectors that makes up a tetrahedron are, (ad),(bd),(cd)
Volume of the Tetrahedron
=[(ad),(bd),(cd)]6=∣ ∣ ∣(4(4))(54)(14)(0(4))((1)4)(14)(3(4))(94)(44)∣ ∣ ∣6=∣ ∣ ∣81(3)4(5)(3)750∣ ∣ ∣6=|7((3)(15))5((24)+12)|6=|5×27×3|=11

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