JEE Advanced 2021 Mathematics question
Let , and be vectors in three-dimensional space, where and are unit vectors which are not perpendicular to each other and
· = 1, · = 1, · = 4
If the volume of the parallelopiped, whose adjacent sides are represented by the vectors , and , is , then the value of is .
Answer: 7
Solution
Let . The square of the volume equals the Gram determinant: . Setting this equal
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