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There are two vectors `vecA= 3hati+hatj and vecB=hatj+2hatk`. For these two vectors - (a) If `vecA & vecB` are the adjacent sides of a parallelogram then find the magnitude of its area. (b) Find a unit vector which is perpendicular to both `vecA & vecB`. |
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Answer» Correct Answer - (a) 7 units (b) `(2)/(7)hati- (6)/(7)hatj+ (3)/(7)hatk` (a) Area of the parallelogram `= |vecA xx vecB| = |{:(hati,,hatj,,hatk),(3,,1,,0),(0,,1,,2):}|` `" "= |2hati-6hatj+3hatk|= sqrt(2^(2)+ (-6)^(2)+ 3^(2))` = 7 units (b) Unit vector perpendicular to both `vecA & vecB` `hatn = (vecAxx vecB)/(|vecAxx vecB|)= (2hati-6hatj+3hatk)/(7)` `= (2)/(7)hati- (6)/(7)hatj+ (3)/(7) hatk` |
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