Important Questions of Vector Algebra Mathematics | Zigya

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11. Let space straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus straight j with hat on top minus 2 straight k with hat on top space and space straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top. space Let space straight c with rightwards arrow on top space be space straight a space vector space such space that space vertical line straight c with rightwards arrow on top minus straight a with rightwards arrow on top vertical line equals 3
vertical line left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space straight x straight c with rightwards arrow on top vertical line space equals space 3 space and space the space angle space between space straight c with rightwards arrow on top space and space straight a with rightwards arrow on top space straight x space straight b with rightwards arrow on top space be space 30 to the power of straight o. space Then space straight a with rightwards arrow on top. straight c with rightwards arrow on top space is space
equal space to space
  • 1/8

  • 25/8

  • 2

  • 2

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12.

If straight u with rightwards arrow on top comma straight v with rightwards arrow on top comma straight w with rightwards arrow on top are non–coplanar vectors and p, q are real numbers, then the equality open square brackets 3 straight u with rightwards arrow on top comma straight p straight v with rightwards arrow on top comma straight p straight w with rightwards arrow on top close square brackets minus open square brackets straight p straight v with rightwards arrow on top comma straight w with rightwards arrow on top comma space straight q straight u with rightwards arrow on top close square brackets space minus space left square bracket 2 straight w with rightwards arrow on top comma straight q straight v with rightwards arrow on top comma straight q straight u with rightwards arrow on top right square bracket space equals space 0 holds for

  • exactly one value of (p, q)

  • exactly two values of (p, q)

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

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

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13.

If open vertical bar straight Z space equals space 4 over straight z close vertical bar, then the maximum value of |Z| is equal to

  • square root of 3 space plus 1
  • square root of 5 space plus 1
  • 2

  • 2

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14.

The vector straight a with rightwards arrow on top space equals space straight alpha space straight i with hat on top space plus 2 straight j with hat on top space plus straight beta straight k with hat on top lies in the plane of the vectors straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top space and space straight c with rightwards arrow on top space equals space straight j with hat on top space plus straight k with hat on top and bisects the angle between straight b with rightwards arrow on top space and space straight c with rightwards arrow on top.Then which one of the following gives possible values of α and β?

  • α = 2, β = 2

  • α = 1, β = 2

  • α = 2, β = 1

  • α = 2, β = 1

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15.

The non−zero verctors straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on topare related by straight a with rightwards arrow on top space equals space 8 straight b with rightwards arrow on top space and space straight c with rightwards arrow on top space equals space minus space 7 straight b with rightwards arrow on top.Then the angle between straight a with rightwards arrow on top space and space straight c with rightwards arrow on top is

  • 0

  • π/4

  • π/2

  • π/2

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16.

If straight u with hat on top space and space straight v with hat on top are unit vectors and θ is the acute angle between them, then  is a 2 straight u with hat on top space and space 3 straight v with hat on topunit vector for 

  • Exactly two values of θ

  • More than two values of θ

  • No value of θ

  • No value of θ

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17.

A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. The angle of projection is-

  • tan to the power of negative 1 end exponent space straight b over ac
  • 45°

  • tan to the power of negative 1 end exponent fraction numerator bc over denominator straight a left parenthesis straight c minus straight a right parenthesis end fraction
  • tan to the power of negative 1 end exponent fraction numerator bc over denominator straight a left parenthesis straight c minus straight a right parenthesis end fraction
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18. Let space straight a with minus on top space equals space straight i with hat on top space plus straight j with hat on top space plus straight k comma space straight b with bar on top space equals space straight i with hat on top space minus straight j with hat on top space plus 2 straight k with hat on top space and space straight c with bar on top space equals space straight x straight i with hat on top space plus space left parenthesis straight x minus 2 right parenthesis straight j with hat on top minus straight k with hat on top.
If space the space vector space straight c with bar on top space lies space in space the space plane space of space straight a with bar on top space and space straight b with bar on top comma space then space straight x space equals
  • 0

  • -1

  • -2

  • -2

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19.

ABC is a triangle, right angled at A. The resultant of the forces acting along AB with rightwards arrow on top space comma space AC with rightwards arrow on top space space with space magnitudes space 1 over AB space and space 1 over AC respectively is the force along AD with rightwards arrow on top where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

  • fraction numerator AB squared space plus space AC squared over denominator left parenthesis AB right parenthesis squared plus left parenthesis AC right parenthesis squared end fraction
  • fraction numerator left parenthesis AB right parenthesis left parenthesis AC right parenthesis over denominator AB space plus space AC end fraction
  • 1 over AB plus 1 over AC
  • 1 over AB plus 1 over AC
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20. If space 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 top enclose straight a space straight x space left parenthesis top enclose straight b space straight x space top enclose straight c right parenthesis comma space where space top enclose straight a comma space top enclose straight b space and space top enclose straight c space are any three vectors such that top enclose straight a. top enclose straight b space not equal to 0 space top enclose straight b. top enclose straight c space not equal to 0 comma space then space straight a with bar on top space and space straight c with bar on top space are
  • inclined at an angle of π/3 between them

  • inclined at an angle of π/6 between them

  • perpendicular

  • perpendicular

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