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If ` vec u ,"" vec v , vec w` are noncoplanar vectors and p, q are real numbers, then the equality `[3 vec u ,""p vec v , p vec w]-[p vec v ,"" vec w , q vec u]-[2 vec w ,""q vec v , q vec u]=0` holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)

A

exactly two values of (p,q)

B

more than two but not all values of (p,q)

C

all values of (p,q)

D

exactly on e value of (p,q)

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The correct Answer is:
D
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DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -2 : CONCEPT APPLICATOR
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  2. If vec x and vec y are two non-collinear vectors and ABC is a triangle...

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  3. If vec u ,"" vec v , vec w are noncoplanar vectors and p, q are re...

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  4. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  5. A non-zero vecto veca is such tha its projections along vectors (hati ...

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  6. veca, vecb ,vec c are three vectors with magnitude |veca| = 4, |vecb|...

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  7. If the two adjacent sides of two rectangles are represented by vect...

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  8. OA, OB, OC are the sides of a rectangular parallelopiped whose diagona...

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  9. If the positive numbers a, b and c are the pth, qth and rth terms of G...

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  10. A vector veca=(x,y,z) makes an obtuse angle with F-axis, and make equa...

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  11. Let vecOB = hati + 2hatj + 2hatk " and" vecOA = 4hati + 2hatj + 2hatk ...

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  12. If a1 , a2 and a3 are three numbers satisfying a1^2 + a2^2 +a3^2 = 1 ,...

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  13. Let veca , vecb and vec c be non coplanar unit vectors equally incl...

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  14. Let veca , vecb, vec c be three non coplanar vectors , and let vecp ,...

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  15. Let veca= 2hati+hatj -2hatk and vecb=hati+hatj. If vec c is a vecto...

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  16. Let vec r , vec a , vec b and vec c be four non zero vectors such tha...

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  17. Let vec r = (veca xx vecb) sin x + (vecb + vec c) cos y + 2 (vec c xx...

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  18. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

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  19. If vec a+vec b+vec c=0, prove that (vec a xx vec b)=(vec b xx vec c)=(...

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  20. If |vec a + vecb| = |vec a - vecb| , then which one of the following i...

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