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Find a such that the vectors (2i – j + k), (i + 2j – 3k) and (3i + aj + 5k) are coplanar.

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Find a such that the vectors (2i – j + k), (i + 2j – 3k) and (3i + aj + 5k) are coplanar.

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Since the vectors (2i – j + k), (i + 2j – 3k) and (3i + aj + 5k) are coplanar,

so,

3(3 – 2) – a(– 6 – 1) + 5(4 + 1) = 0

3 + 7a + 25 = 0

7a = – 28

a = – 4

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