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Calculus - Linear Operators - Vectors - Equation of a plane

Question (1):
Find the equation of the plane containing the vector a = (3 , - 2 , - 1 ) and parallel to the vectors b = (1, - 2 , 4 ) and c = (3 , 2 , - 5 )

Question (2) :
Find the equation of a plane passing through A and B whose position vectors are
4i + j - 2k , 5i + 2j + k respectively and parallel to the vector 3i - j + 4 k.

Question (3) :
Show that the lines r = (i - j) + lamda (2 i + k) and r = (2i - j) + mu(i + j - k) do not intersect.

Solution Preview

Solution (1)
The formula is [ r , b, c ] = [ a, b, c]
Therefore, the required equation of the plane is 2 x + 17 y + 8z + 36 = 0
( for complete step by step ...

Solution Summary

Solutions to the posted problems are given with step by step explanation and complete working so that the student could easily understand the procedure to work out such problems. These solutions can be even used as model solutions to solve other similar type of problems.

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