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The cartesian equation of a line is (x-3...

The cartesian equation of a line is `(x-3)/(2)=(y+1)/(-2)=(z-3)/(5).` Find the vector equation of the line.

Text Solution

Verified by Experts

The correct Answer is:
`r=3hat(i)-hat(j)+3hat(k)+lambda(2hat(i)-2hat(j)+5hat(k))`
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The Cartesian equation of a line is (x+3)/(2)=(y-5)/(4)=(z+6)/(2). Find the vector equation for the line.

The Cartesian equations of a line are (x-3)/(2)=(y+2)/(-5) =(z-6)/(4) Find the vector equations of the line .

Knowledge Check

  • The Cartesian equations of a line are (x-1)/(2)=(y+2)/(3) =(z-5)/(-1) . Its vector equations is

    A
    `vec(r ) =(-hat(i) +2hat(j) -5hat(k)) + lambda (2hat(i) +3hat(j) -hat(k))`
    B
    `vec(r )=(2hat(i) +3hat(j) -hat(k)) +lambda (hat(i)-2hat(j) +5hat(k))`
    C
    `vec(r )=(hat(i) -2hat(j) +5hat(k)) +lambda (2hat(i) +3hat(j)-4hat(k))`
    D
    none of these

  • The Cartesian equations of a line are (x-2)/(2)=(y+1)/(3) =(z-3)/(-2) .What is its vector equations ?

    A
    `vec(r ) =(2hat(i) +3hat(j) -2hat(k)) +lambda (2hat(i) -hat(j) +3hat(k))`
    B
    `vec(r )=(2hat(i) -hat(j) +3hat(k)) +lambda (2hat(i) +3hat(j) -2hat(k))`
    C
    `vec(r ) =(2hat(i) +3hat(j) -2hat(k))`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    The Cartesian equations of a line are (x-1)/(2)=(y+2)/(3)=(5-z)/(1) . Find its vector equation.

    The Cartesian equation of a line is (x-5)/3=(y+4)/7=(z-6)/2. find the vector equation of the line.

    The cartesian equation of a line is (x+2)/(1) = (y+3)/(-2) = (z)/(3) , find its vector equation.

    The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2) Write its vector form.

    The cartesian equation of a line is (x - 6) /(2) = ( y + 4)/(7) = (z -5)/(3) , find its vector equation .

    The cartesian equations of line is : (x - 1)/(2) = (y - 2)/(3) = (z -3)/(4) . Write the vector equation.

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