Vectors 3 Question 14

14. Let a,b,c be distinct non-negative numbers. If the vectors ai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ lie in a plane, then c is

(1993, 1M)

(a) the arithmetic mean of a and b

(b) the geometric mean of a and b

(c) the harmonic mean of a and b

(d) equal to zero

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Answer:

Correct Answer: 14. (b)

Solution:

  1. Since, three vectors are coplanar.

|aac101ccb|=0

Applying C1C1C2,|0ac 101 0cb|=0

1(abc2)=0ab=c2



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