3-D Geometry Class - 12 || Vector & Cartesian form of a straight line

Let vec n be a vector of magnitude 2sqrt(3) such that it makes equal acute angles with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane passing through (1,-1,2) and normal to vec ndot

If vec n is a vector of magnitude sqrt(3) and is equally inclined with an acute angle with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane which passes through (2, 1, -1) and is normal to vec n .

A plane passes through the point (1,-2,5) and is perpendicular to the line joining the origin to the point 3 hat i+ hat j- hat kdot Find the vector and Cartesian forms of the equation of the plane.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2 hat i- hat j+4 hat k and is in the direction hat i+2 hat j- hat k .

When a body moved along a straight line from A to B its velocity vector is represented by a straight line - directed from A to B . But " when the same body rotates in circular path is velocity vector is represented by a straight line perpendicular to the plane of the circular path " . Why ?

Find the vector form as well as in Cartesian form, the equation of the line passing through the points A(1,\ 2,-1)a n d\ B(2,\ 1,\ 1)dot

Find the vector and cartesian equation of a line passes through the points (1,3,2) and origin.

Find the equations of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intercepted between the axes of coordinates.

Class 12 chapter vector algebra topic dot or scalar product