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Vectors

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Anvita Mahajan

7 Years agoGrade

1 Answer

Samyak Jain

7 Years ago

c is parallel to the plane of a and b. We study free vectors in maths i.e. vectors that are movable. So,

a, b, c lie in one plane. Then (a x b) . c = 0 i.e. [a b c] = 0, where [a b c] is determinant of a, b, c.

a = i – 2j + 3k, b = 3i + 3j – k, c = d i + j + (2d – 1)k

Solving determinant, we get 1(6d – 3 + 1) + 2(6d – 3 + d) + 3(3 – 3d) = 0.

6d – 2 + 14d – 6 + 9 – 9d = 0 $\Rightarrow$ 11d + 1 = 0 $\Rightarrow$ 11d = – 1

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