Vectors 3 Question 15

15. Let a=a1i^+a2j^+a3k^,a=b1i^+b2j^+b3k^ and a=c1i^+c2j^+c3k^ be three non-zero vectors such that c is a unit vector perpendicular to both the vectors c and b. If the angle between a and b is π6, then |a1a2a3 b1b2b3 c1c2c3|2 is equal to

(1986, 2M)

(a) 0

(b) 1

(c) 14(a12+a22+a32)(b12+b22+b32)

(d) 34(a12+a22+a32)(b12+b22+b32)(c12+c22+c32)

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Answer:

Correct Answer: 15. (c)

Solution:

  1. Since, (a×b)=|a||b|sinπ6n^

(a×b)c=12|a||b|n^c[abc]=12|a||b|cos0

n^ is perpendicular to both a,b and c is also a unit vector perpendicular to both a and b.

|a1a2a3 b1b2b3 c1c2c3|2=[abc]2=14|a|2|b|2 =14(a12+a22+a32)(b12+b22+b32)



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