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QUESTION: 1

Let be the position vector of an arbitrary point P(x, y, z). Cartesian form of the equation of line passes through two points (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) is:

Solution:

QUESTION: 2

Find the vector equation of the line that passes through the origin and (-6,2,1).

Solution:

QUESTION: 3

The Cartesian equation of the line which passes through the point (2, -2, -1) and parallel to the line , is given by

Solution:

QUESTION: 4

If the vector equation of a line is find its caryesian equation.

Solution:

r = -2i + 3j + 7k + λ( -i - 2j - 3k)

xi + yj + zk = (-2-λ)i + (3-2λ)j + (7-3λ)k

Equating the terms, we get

x = -2-λ y = 3-2λ z = 7-3λ

(x+2)/(-1) = λ, (y-3)/(-2) = λ, (z-7)/(-3) = λ

(x+2)/(1) = (y-3)/(2) = (z-7)/(3)

QUESTION: 5

The vector form of the equation is. The Cartesian equation of the line is:

Solution:

QUESTION: 6

Let the coordinates of the given point A be (x_{1}, y_{1}, z_{1}) and the direction ratios of the line be a, b, c. If the co-ordinates of any point P is (x, y, z), then the equation of the line in Cartesian form is:

Solution:

QUESTION: 7

Let be a position vector of A with respect to the origin O and be a position vector of an arbitrary point. The equation of line which passes through A and parallel to a vector is:

Solution:

QUESTION: 8

The Cartesian equation of the line passing through the points (-3, 1, 0) and (1, 2, 3) is:

Solution:

QUESTION: 9

The Cartesian equation of the line which passes through the origin and parallel to the line , is given by

Solution:

QUESTION: 10

Find the Cartesian equation of the line that passes through the point (-3,-4,-2) and (3,4,2).

Solution:

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