KCET2007MathematicsVector Algebra

If a =2 i +3 j - k , b = i +2 j -5 k , c =3 i +5 j - k , then a vector perpendicular to a and in the plane containing b and c is

Options

A-17 i +21 j -97 k
B17 i +21 j -123 k
C-17 i -21 j +97 k
D-17 i -21 j -97 k

Correct answer

D. -17 i -21 j -97 k

Step-by-step solution

We know that a vector perpendicular to a and in the plane containing b and c is given by b c = | array ccc i & j & k 1 & 2 & -5 3 & 5 & -1 array | Now, a ( b c )= | array ccc i & j & k 2 & 3 & -1 23 & -14 & -1 array | which is the required vector.

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