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If bar(i), bar(j), bar(k) are unit vecto...

If `bar(i), bar(j), bar(k)` are unit vectors along the positive directions of the coordinate axes, then shown that the four points `4 bar(i) + 5 bar(j) + bar(k), - bar(j) - bar(k), 3 bar(i) +9 bar(j) + 4 bar(k) and - 4 bar(i) + 4 bar(j) + 4 bar( k)` are coplanar

Text Solution

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The correct Answer is:
`bar(PQ),bar(PR),bar(PS)`
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Explore conceptually related problems

Prove that vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) -bar(3j)-5bar(k) and bar(c ) = 3bar(i) - 4bar(j) -4bar(k) are coplanar.

Find the vector equation of the plane passing through the points bar(i) - 2 bar(j) + 5 bar(k), - 5 bar(j) - bar(k) and - 3 bar(i) + 5 bar(j)

Knowledge Check

  • The volume of a tetrahedron whose vertices are 4 bar(i) + 5 bar(j) + bar(k), - bar(j) + bar(k) , 3 bar(i) + 9 bar(j) + 4 bar(k) and - 2 bar(i) + 4 bar(j) + 4 bar(k ) is (in cubic units)

    A
    `(14)/(3)`
    B
    `5`
    C
    `6`
    D
    `30`
  • A point lying on the plane that passes through the points bar(i) + bar(j) + bar(k), bar(i) - 2 bar(j) + 3 bar(k) and bar(i) + 2 bar(j) - 3 bar(k) is

    A
    `- bar(i) + 2 bar(j)- 3 bar(k)`
    B
    `- bar(i) + bar(j) - bar(k)`
    C
    `bar(i) + bar(j) - bar(k)`
    D
    `4 bar(i) + 2 bar(j) + 3 bar(k)`
  • The four points 2bar(i)+3bar(j)-bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+4bar(j)-2bar(k), bar(i)-6bar(j)+6bar(k) are

    A
    Collinear
    B
    Coplanar but non collinear
    C
    non coplanar
    D
    cannot be determined
  • Similar Questions

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