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Let x and y be two vectors in a three-dimensional space and < x, y > denote their dot product. Then the determinant, 
  • a)
    zero when x and y are linearly independent
  • b)
    positive when x and y are linearly independent
  • c)
    non-zero for all non-zero x and y
  • d)
    zero only when either x or y is zero
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let x and y be two vectors in a three-dimensional space and < x, y ...

and let 

So,  

Now, on putting
D = 0 or

Vector   are linearly dependent.
So, linearly dependent ⇒ D = 0 and for linearly independent ⇒ D ≠ 0
or Positive and negative
We can also see that D = (x2y1 - x1y2)2 cannot be negative.
So, linearly independent ⇒ D is positive.
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Most Upvoted Answer
Let x and y be two vectors in a three-dimensional space and < x, y ...

and let 

So,  

Now, on putting
D = 0 or

Vector   are linearly dependent.
So, linearly dependent ⇒ D = 0 and for linearly independent ⇒ D ≠ 0
or Positive and negative
We can also see that D = (x2y1 - x1y2)2 cannot be negative.
So, linearly independent ⇒ D is positive.
Free Test
Community Answer
Let x and y be two vectors in a three-dimensional space and < x, y ...

and let 

So,  

Now, on putting
D = 0 or

Vector   are linearly dependent.
So, linearly dependent ⇒ D = 0 and for linearly independent ⇒ D ≠ 0
or Positive and negative
We can also see that D = (x2y1 - x1y2)2 cannot be negative.
So, linearly independent ⇒ D is positive.
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Let x and y be two vectors in a three-dimensional space and < x, y > denote their dot product. Then thedeterminant,a)zero when x and y are linearly independentb)positive when x and y are linearly independentc)non-zero for all non-zero x and yd)zero only when either x or y is zeroCorrect answer is option 'B'. Can you explain this answer?
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