Home
Class 12
MATHS
A line passes through the point with pos...

A line passes through the point with position vector `2hat(i)-3hat(j)+4hat(k)` and is in the diretion of `3hat(i)+4hat(j)-5hat(k)`. Find the equation of the line is vector and cartesian forms.

Text Solution

Verified by Experts

The correct Answer is:
`r=2hat(i)-3hat(j)+4hat(k)+lambda(3hat(i)+4hat(j)-5hat(k)), (x-2)/(3)=(y+3)/(4)=(z-4)/(-5)`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 3|15 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 1|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find equations of the line in vector and Cartesian form.

A line passes through the point with position vector 2hat i-3hat j+4k is in the direction of 3hat i+4hat j-5hat k. Find the equations of the line in vector and Cartesian forms.

Find the vector equations of the line passing through the point with position vector (2hat(i) +hat(j) -5hat(k)) and parallel to the vector (hat(i) +3hat(j) -hat(k)) .Deduce the Cartesian equations of the line .

A line is drawn in the direction of (hat(i) +hat(j) -2hat(k)) and it passes through a point with position vector (2hat(i) -hat(j) - 4hat(k)) .Find the equations of the line in the vector as well as Cartesian forms.

Find the vector equation of a line which passes through the point with position vector 2hat i=hat j+4hat k and is in the direction of hat i+hat j-2hat k .Also,reduce it to Cartesian form.

Find the vector equation of a line passing through the point with position vector 2hat(i) + hat(j) - hat(k) and parallel to the line joining the points - hat(i) + hat(j) + 4 hat(k) and hat(i) + 2 hat(j) + 2 hat(k) .

A line passes through the point (3,4,5) and is parallel to the vector (2hat(i) +2hat(j) -3hat(k)) . Find the equations of the line in the vector as well as Cartesian forms.

Find the Cartesian equation of a line which passes through the point having position vector (2hat(i) -hat(j) + 4hat(k)) and is in the direction of the vector , (hat(i) +2hat(j) -hat(k))

(i) Find the vector equation of a line passing through a point with position vector 2 hat(i) - hat(j) + hat(k) and parallel to the line joining the points with position vectors - hat(i) + 4 hat(j) + hat(k) and hat(i) + 2 hat(j) + 2 hat(k). Also, find the cartesian equivalent of the equation. (ii) Find the vector equation of a line passing through the point with position vector hat(i) - 2 hat(j) - 3 hat(k) and parallel to the line joining the points with position vectors hat(i) - hat(j) + 4 hat(k) and 2 hat(i) + hat(j) + 2 hat(k) . Also, find the cartesian form of the equation.

A line passes through the point A(5,-2.4) and it is parallel to the vector (2hat(i) -hat(j) +3hat(k)) .The vector equations of the line is