Let a , b and c be distinct positive numbers. If the vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c…

Let a,b and c be distinct positive numbers. If the vectors ai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ are co-planar, then c is equal to:
  1. 21a+1b
  2. a+b2
  3. 1a+1b
  4. ab

Solution

Given vectors ai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ are co-planar, then

aac101ccb=0

⇒a0-c-ab-c+cc-0=0

⇒c2=ab

⇒c=ab.

Asked in: JEE Main 2021 (25 Jul Shift 2)

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