Test: Cartesian Equation Of A Line


10 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Cartesian Equation Of A Line


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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 (x1, y1, z1) and (x2, y2, z2) 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 (x1, y1, z1) 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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