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Prove that the vectors 2hat(i) - hat(j) ...

Prove that the vectors `2hat(i) - hat(j) + hat(k), hat(i) - 3hat(j) - 5hat(k), 3hat(i) - 4hat(j) - 4hat(k)` are the sides of a right angled triangle.

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Show that the vectors 2hat(i) + 3hat(j), 5hat(i) - 5hat(k) and 6hat(j) + 4hat(k) are coplanar.

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

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.