Question

if vectors 2i+2j-2k, 5i+yj+k and -i+2j+2k are coplanar, find y

Answer 1

Answer:

23

Explanation:

We can check if these vectors are coplanar by triple scalar product.

let a = 2i + 2j - 2k

b = 5i + yj + k

c = -i + 2j + 2k

Triple dot product = b . [a x c]

[a x c] = (8i - 2j + 6k)

b. [a x c] = (5i + yj + k)(8i -2j + 6k) = 40 - 2y + 6 = 0

=>  2y = 46

=> y = 23

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