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Show that the vectors hati-hatj-hatk,2ha...

Show that the vectors `hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk` are coplanar.

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Show that the vectors hati-3hatj+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

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Using scalar triple product, show that the four points given by position vectors : 2hati+3hatj+2hatk,4hati-5hatk,3hati+hatj-2hatk and 5hati+3hatj-4hatk are coplanar.

Show that the three points with position vectors hati+2hatj+7hatk , 2hati+6hatj+3hatk and 3hati+10hatj-hatk are collinear.

Find the value of lambda . such that given vectors 3hati+lambdahatj+5hatk , hati+2hatj-3hatk and 2hati-hatj+hatk are coplaner.