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If overset(to)(a) =hat(i) - hat(k) , o...

If `overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + hat(j) + (1-x) hat(k)` and
`overset(c ) =y hat(i) +x hat(j) + (1+x-y) hat(k) . "Then " [overset(to)(a) , overset(to)(b) , overset(to)( c) ]` depends on

A

only x

B

only y

C

neither x nor y

D

both x and y

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The correct Answer is:
C
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If vec(a) = hat(i)- hat(k) , vec(b) = x hat(i) + hat(j) + (1-x) hat(k), vec(c ) = y hat(i) + x hat(j) + (1+ x- y)hat(k) then vec(a).(vec(b) xx vec(c )) depends on

Let overset(to)(a) =hat(i)+2hat(j)+hat(k),overset(to)(b) =hat(i)-hat(j)+hat(k),overset(to)(C )=hat(i)+hat(j) -hat(k). A vector coplanar to overset(to)(a) and overset(to)(b) has a projections along overset(to)(c ) of magnitude (1)/(sqrt(3)) then the vector is

Let overset(to)(a) =2hat(i) +hat(j) + hat(k), overset(to)(b) =hat(i) + 2hat(j) -hat(k) and a unit vector overset(to)(c ) be coplanar. If overset(to)(c ) is perpendicular to overset(to)(a) " then " overset(to)(c ) is equal to

Let overline(a)=hat(i)-hat(k), overline(b)=xhat(i)+hat(j)+(1-x)hat(k), overline(c)=yhat(i)+xhat(j)+(1+x-y)hat(k) . Then [[overline(a), overline(b), overline(c)]] depends on

Let overset(to)(a) = hat(i) - hat(j) , overset(to)(b) - hat(k) , overset(to)( c) - hat(k) - hat(i) . If overset(to)(d) is a unit vector such that overset(to)(a) , Overset(to)(d) =0= [ overset(to)(b) overset(to)(c ) overset(to)d)] then overset(to)(d) equals

If overset(to)(a) " and " overset(to)(b) are vectors in space given by overset(to)(a) = (hat(i) -2hat(j))/(sqrt(5)) " and " overset(to)(b) = (2hat(i) + hat(j) +3hat(k))/(sqrt(14)) then the value of (2overset(to)(a) + overset(to)(b)).[(overset(to)(a) xx overset(to)(b)) xx (overset(to)(a) -2overset(to)(b))] is .........

Let overset(to)(a) =2hat(i) + hat(j) -2hat(k) " and " overset(to)(b) = hat(i) + hat(j) . " If " overset(to)(c ) is a vectors such that |overset(to)(a)"." overset(to)(c ) = |overset(to)( c)| , |overset(to)(c )- overset(to)(a)|= 2sqrt(2) and the angle between (overset(to)(a) xx overset(to)(b)) " and " overset(to)( c ) " is " 30^(@), " then "|(overset(to)(a) xx overset(to)(b)) xx overset(to)( c )| is equal to

If overset(to)(a) = (hat(i) + hat(j) + hat(k)) , overset(to)(a) , overset(to)(b) , overset(to)(c ) =1 " and " overset(to)(a) xx overset(to)(b) = hat(j) - hat(k), " then " overset(to)(b) is equal to

Let overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(a) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(a) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k) be three non- zero vectors such that overset(to)(c ) is a unit vectors perpendicular to both the vectors overset(to)(c ) and overset(to)(b) . If the angle between overset(to)(a) " and " overset(to)(n) is (pi)/(6) then |{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}| is equal to

TARGET PUBLICATION-VECTORS-Critical Thinking
  1. If 2bara+barb=3barc, then A divides BC in the ratio

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  2. In DeltaABC, P is the mid point of BC,Q divides CA internally in the r...

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  3. If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + ...

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  4. If the points (1,1,2),(2,1,p),(1,0,3) and (2,2,0) are co-planar then ...

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  5. If the points A, B, C and D with position vectors overset(^)i+overset(...

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  6. If aoverset(^)i+overset(^)j+overset(^)k,overset(^)i-boverset(^)j+overs...

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  7. If the given vectors (-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac) and (a^2+a...

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  8. If bara,barb,barc are non-zero, non collinear vectors, then the vector...

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  9. Given vectors bara,barb,barc such that bara.(barbxxbarc)=lambda!=0 the...

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  10. For any three vectors bara,barb and barc,(bara-barb)[(barb+barc)xx(bar...

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  11. If bara,barb and barc are three non-coplanar vectors, then : (bara + b...

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  12. If bar r=l(bar b xx bar c)+m(bar c xx bar a)+n(bar a xx bar b) and [...

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  13. The volume of parallelopiped with vector bara+2barb-barc,bara-barb and...

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  14. If the volume of parallelopiped with coterminus edges -poverset(^)i+5k...

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  15. If the volumes of tetrahearon where vertices (1,2,0),(2,0,4),(-1,2,0) ...

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  16. If D is the mid -point of side AB of DeltaABC, then bar(AB) + bar(BC)...

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  17. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

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  18. If G and Gprime are the centroids of the triangle ABC and AprimeBprime...

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  19. If S is circumcentre, O is orthocentre of DeltaABC, then vec(SA)+vec(...

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  20. If A(-3,-2,0),B(3,-3,1) and C(5,0,2) are three successive vertices of...

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