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Find unit vector parallel to the XOY-pla...

Find unit vector parallel to the XOY-plane and perpendicular to the vector `4bar(i) - 3bar(j) + bar(k)`.

Text Solution

Verified by Experts

The correct Answer is:
`pm((3veci+4vecj))/(5)`.
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Explore conceptually related problems

Find a unit vector perpendicular to the plane containing the vector bar(a) = 4bar(i) + 3bar(j) - bar(k), bar(b) = 2bar(i) - 6bar(j) - 3bar(k)

Find the Cartesian equation of the plane passing through the point (-2,1,3) and perpendicular to the vector 3bar(i) + bar(j) + 5bar(k) .

Knowledge Check

  • A line L is passing through the point A whose position vector is bar(i) + 2 bar(j) + 3 bar(k) and parallel to the vector 2 bar(i) + bar(j) + 2 bar(k) . A plane pi is passing through the points bar(i) + bar (j) + bar(k) , bar(i) - bar(j) - bar(k) and parallel to the vector bar(i) - 2 bar(j) . Then the point where this plane pi meets the line L is

    A
    `(1)/(3) ( - 7 bar(i) + bar(j) - 19 bar(k) )`
    B
    `7 bar(i) + bar(j) - 19 bar(k)`
    C
    `3 bar(I) + 3 bar (j) - bar(k)`
    D
    `2 bar(j)- bar(j) + bar(k)`

  • The vector that is parallel to the vector 2bar(i) -2 bar(j) - 4 bar(k) and coplanar with the vectors bar(i) + bar(j) and bar(j) + bar(k) is

    A
    `bar(i) - bar(k)`
    B
    `bar(i) + bar(j) - bar(k)`
    C
    `bar(i) - bar(j) - 2bar(k)`
    D
    `3 bar(i) + 3 bar(j) + 6 bar(k)`

    • Similar Questions

    Explore conceptually related problems

    A non-zero vector bar(a) , is parallel to the line of intersection of the plane determined by the vectors bar(i), bar(i) + bar(j) and the plane determined by the vectors bar(i)- bar(j), bar(i) + bar(k) Find the angle between bar(a) and the vector bar(i)- 2bar(j) + 2bar(k)

    Find the vector equation of the plane which passes through the points 2 bar(i)+ 4 bar(j) + 2 bar(k), 2 bar(i) + 3 bar(j) + 5 bar(k) and parallel to the vector 3 bar(i) - 2 bar(j) + bar(k) . Also find the point where this plane meets the line joining the points 2 bar(i) + bar(j) + 3 bar(k) and 4 bar(i) - 2 bar(j) + 3 bar(k)

    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)

    Find the equation of the line parallel to the vector 2 bar(i) - bar(j) + 2 bar(k) and which passes through the point A whose position vector is 3 bar(i) + bar(j) - bar(k) . If P is a point on this line such that AP = 15, find the position vector of P .

    Find the unit vector in the direction of the sum of the vectors bar(a) = 2bar(i)+ 2bar(j) - 5bar(k) and bar(b) = 2bar(i) + bar(j) + 3bar(k) .

    Find the vector equation of the line passing through the point 2 bar(i) + 3 bar(j) + bar(k) and parallel to the vector 4 bar(i) - 2 bar(j) + 3 bar(k)

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