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 Multiple Choice QuestionsMultiple Choice Questions

31.

A particle is acted upon by constant forces 4 space straight i with hat on top space plus straight j with hat on top space minus 3 straight k with hat on top space space and 3 space straight i with hat on top space plus straight j with hat on top space minus straight k with hat on top which displace it from a point straight i with hat on top space plus 2 straight j with hat on top space plus 3 straight k with hat on top space to space the space point space 5 straight i with hat on top space plus space 4 straight j with hat on top space plus straight k with hat on top. space The work done in standard units by the forces is given by 

  • 40

  • 30

  • 25

  • 25

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32. If space straight a with bar on top comma space straight b with bar on top comma straight c with bar on top space are non-coplanar vectors and λ is a real number, then the vectors straight a with bar on top space plus 2 straight b with bar on top space plus 3 straight c with bar on top space comma space straight lambda straight b with bar on top space plus 4 space straight c with bar on top space and space left parenthesis 2 straight lambda space minus 1 right parenthesis straight c with bar on top are non-coplanar for
  • all values of λ

  • all except one value of λ

  • all except two values of λ

  • all except two values of λ

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33.

Let straight u with bar on top comma space straight v with bar on top space comma space straight w with bar on top be such that vertical line top enclose straight u vertical line space equals space vertical line top enclose straight v vertical line space equals space 2 comma space vertical line top enclose straight w vertical line space equals space 3 If the projection top enclose straight v space along space top enclose straight u  is equal to that of space top enclose straight w space along space top enclose top enclose straight u end enclose space and space top enclose straight v comma space top enclose straight w space are perpendicular to each other then vertical line top enclose straight u space minus top enclose straight v space plus top enclose straight w vertical line equals

  • 2

  • square root of 14
  • square root of 12
  • square root of 12


B.

square root of 14
vertical line top enclose straight u vertical line space equals space 1 comma space vertical line top enclose straight v vertical line space equals space 2 comma space vertical line top enclose straight w vertical line space equals space 3
projection space of space top enclose straight v space along space straight u with rightwards arrow on top space equals fraction numerator straight v with rightwards arrow on top. straight u with rightwards arrow on top over denominator vertical line top enclose straight u vertical line end fraction

projection space of space top enclose straight u space along space straight w with rightwards arrow on top space equals space fraction numerator straight w with rightwards arrow on top. straight u with rightwards arrow on top over denominator vertical line straight u with rightwards arrow on top vertical line end fraction
rightwards double arrow stack straight v. with rightwards arrow on top straight u with rightwards arrow on top space equals space straight w with rightwards arrow on top. straight u with rightwards arrow on top
and space straight v with rightwards arrow on top comma straight w with rightwards arrow on top space are space perpendicular space to space each space other
therefore space straight v with rightwards arrow on top comma straight w with rightwards arrow on top space equals space 0
vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space vertical line straight u with rightwards arrow on top vertical line squared space plus space vertical line straight v with rightwards arrow on top vertical line squared space plus vertical line straight w with rightwards arrow on top vertical line squared space minus 2 straight u with rightwards arrow on top. straight v with rightwards arrow on top space plus 2 straight u with rightwards arrow on top. straight w with rightwards arrow on top space minus space 2 straight v with rightwards arrow on top. straight w with rightwards arrow on top
vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space space equals space 1 plus 4 plus 9 space minus 2 straight u with rightwards arrow on top. straight v with rightwards arrow on top space plus 2 straight v with rightwards arrow on top space. straight u with rightwards arrow on top
vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space 1 plus 4 plus 9
vertical line straight u with rightwards arrow on top minus straight v with rightwards arrow on top space plus straight w with rightwards arrow on top vertical line squared space equals space square root of 14
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34.

Let top enclose straight a space comma top enclose straight b space and space top enclose straight c space be non-zero vectors such that left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x space top enclose straight c space equals space 1 third space vertical line straight b with bar on top vertical line vertical line straight c with bar on top vertical line vertical line straight a with bar on top vertical line If θ is the acute angle between the vectors top enclose straight b space and space top enclose straight c comma then sin θ equals

  • 1/3

  • fraction numerator square root of 1 over denominator 3 end fraction
  • 2/3

  • 2/3

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35.

Let u be a vector coplanar with the vectors a a = 2i^ + 3j^ -k^ and b = j^ +k^.  if u is perpendicular to a and u.b = 24, then |u| is equal to:

  • 84

  • 336

  • 315

  • 256


36.

The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is:

  • 23

  • 23

  • 2/3

  • 1/3


37.

For any vector x, where i, j, k have their usual meanings the value of x × i^2 + x × j^2 + x × k^2 where i^, j^, k^ have their usual meanings, is equal to

  • x2

  • 2x2

  • 3x2

  • 4x2


38.

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

  • 2 units

  • 2 units

  • 3 units

  • 5 units


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39.

For non-zero vectors a and b, if a + b < a - b,  then a and b are

  • collinear

  • perpendicular to each other

  • inclined at an acute angle

  • inclined at an obtuse angle


40.

Which of the following is not always true?

  • a + b2 = a2 + b2, if a and b are perpendicular to each other

  • a + λb  a for all λ  R,  if a and b are perpendicular to each other

  • a + b2 +a - b2 = 2a2 + b2

  • a + λb  a for all λ  R, if a is parallel to b


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