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Determine k such that a vector vec(r) is...

Determine k such that a vector `vec(r)` is at right angles to each of the vectors `vec(a) = k hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - k hat(k)` and `vec(c) = -2hat(i) + k hat(j) + 3hat(k)`.

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The correct Answer is:
k = 0
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Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

Show that the vectors vec(a) = 3hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) - 3hat(j) + 5hat(k) and vec(c) = 2hat(i) + hat(j) - 4hat(k) form a right angled triangle.