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The Cartesian equation of a line is (...

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 equation of a line is (x-1)/(3)=(y-4)/(5)=(z-3)/(2) . Write its vector form.

Knowledge Check

  • Vector equation of the line (x+1)/(2)=(y-4)/(4)=(z+6)/(3)

    A
    `vec(r)=(hat(i)-4hat(j)+6hat(k))+lamda(2hat(i)+4hat(j)+3hat(k))`
    B
    `vec(r)=(-hat(i)+4hat(j)-6hat(k))+lamda(2hat(i)+4hat(j)+3hat(k))`
    C
    `vec(r)=(2hat(i)+4hat(j)+3hat(k))+lamda(hat(i)-4hat(j)+6hat(k))`
    D
    `vec(r)=(2hat(i)+4hat(j)+3hat(k))+lamda(-hat(i)+4hat(j)-6hat(k))`

    • Similar Questions

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    If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4 , write the vector equation for the line.

    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 6x - 2 = 3y + 1 = 2z - 2 . Find :(a) the direction-ratios of the line, and (b) vector equation of the line parallel to this line and· passing through the point (2, - 1, - 1).

    The Cartesian equations of a line are (x-5)/3 = (y+4)/7 =(z-6)/2 . Vector equation for the line is vecr =(5hati + 4hatj + 6hatk)+ lambda(3hati +7hatj + 2hatk)

    If the equation of line AB is (x-3)/(1)=(y+2)/(-2)=(z-5)/(4) , find the direction of a line parallel to AB.

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    The cartesian equations of a line are : (x-5)/3=(y+4)/7=(z-6)/2 and (x+3)/2=(y-5)/4=(z+6)/2 . find the vector equation of the lines.

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