Question

find the cartesian equation of the following line given in vector form r=(2i+j-4k)+lambda(i-j-k)​

Answer 1

Given:  r = ( 2i + j - 4k ) + λ ( i - j - k ) ​

To find: The cartesian equation of the following line given.

Solution:

• Now the equation given is  r = ( 2i + j - 4k ) + λ ( i - j - k ) ​

• This is the vector form of a line.Now direction ratio of the above equation are (1, -1,-1).

• The point through which the line passes is (2, 1, –4).

• Now the cartesian equation of the following line given will be:

                    x - x1 / a = y - y1 / b = z - z1 / c

• Putting the values in formula, we get:

                    x - 2 / 1 = y - 1 / -1 = z + 4 / -1

                    x - 2 = 1 - y = -z - 4

Answer:

       The cartesian equation of the following line given is x - 2 = 1 - y = -z - 4