Find the unit vector perpendicular to the plane containing the vectors ] = (41+ 21 - k) and Q = (3î – ĵ + k). Also find the area of the parallelogram formed by the two vectors.

Find the unit vector perpendicular to the plane containing the vectors

1.	Find the unit vector perpendicular to the plane containing the vectors ] = (41+ 21 - k) and Q = (3î – ĵ + k). Also find the area of the parallelogram formed by the two vectors.
Answer» We know that a×B is VECTOR perpendicular to the plane of a and bTherefore unit vector perpendicular to the plane of a and b = ∣a×b∣a×b Now a×b=(2i−j+K)×(3i+4j−k)= ∣∣∣∣∣∣∣∣ i23 j−14 k1−1 ∣∣∣∣∣∣∣∣ =i(1−4)+j(3+2)+k(8+3)=−3i+5j+11k⇒ unit vector PARALLEL to a×b= ∣a×b∣a×b = (3 2 +5 2 +11 2 ) −3i+5j+11k = 155 −3i+5j+11k

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Find the unit vector perpendicular to the plane containing the vectors ] = (41+ 21 - k) and Q = (3î – ĵ + k). Also find the area of the parallelogram formed by the two vectors.​

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Find the unit vector perpendicular to the plane containing the vectors ] = (41+ 21 - k) and Q = (3î – ĵ + k). Also find the area of the parallelogram formed by the two vectors.