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Equation of Line
Question 1
What is the primary characteristic of the slope-intercept form of a line?
It defines a line using two points.
It expresses a line in terms of its slope and y-intercept.
It uses direction ratios to describe the line.
It represents a line through its normal vector.
Question 2
In the Cartesian form of a line in 3D space, which of the following represents the relationship between the coordinates of two points on the line?
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁) = (z - z1)/(z2 - z1)
(x - x₁)/(y₂ - y₁) = (y - y₂)/(x₂ - x₁)
(x - y₁)/(y - x₂) = (z - z₁)/(z₂ - z₁)
(x + x₁)/(x₂ + y₁) = (y + y₂)/(z - z₁)
Question 3
Which of the following describes the normal form of a line in relation to the angle it makes with the x-axis?
y = mx + b
x cos θ + y sin θ = p
(x - x₁)/(x₂ - x₁) = (y - y₁)/(y₂ - y₁)
(x + y + z)/p = 1
Question 4
In vector form, how is the equation of a line through two points A and B represented?
r = a + λ(b - a)
r = a + b + λd
r = (x₀ + t a, y₀ + t b, z₀ + t c)
r = (x₁, y₁, z₁) + t(a, b, c)
Question 5
Which form is best suited for describing a line with known x- and y-intercepts?
x/a + y/b = 1
y = mx + b
ax + by + c = 0
r = a + λ(b − a)
Question 6
What is the vector equation of a line passing through the point (2, 1, 3) and parallel to the vector 3𝑖 − 2𝑗 + 𝑘?
r = 2i - j - 3k - λ(3i − 2j + k)
r = 2i + j + 3k + λ(3i − 2j + k)
r = 2i + j + 3k - λ(3i − 2j + k)
r = 2i + j + 3k + λ(3i + 2j + k)
Question 7
A line passes through the point (1, 2, 3) and is parallel to the vector v = 4, -5, 6 Determine the point of intersection of this line with the plane defined by the equation (2x - y + z = 7).
[Tex]{\left(\frac{27}{19}, \frac{28}{19}, \frac{69}{19}\right)}[/Tex]
[Tex]{\left(\frac{29}{19}, \frac{36}{19}, \frac{69}{19}\right)}[/Tex]
[Tex]{\left(\frac{2}{19}, \frac{8}{19}, \frac{9}{19}\right)}[/Tex]
None
Question 8
Find the equation of the line that passes through the point (2, −3) and is parallel to the line passing through the points (5, 1) and (7, 5).
y = 2x - 7
y = 2x + 7
y = 7x - 2
y = 7x + 2
Question 9
Find the equation of the line that makes an angle of 60∘ with the positive direction of the x-axis and cuts off an intercept of 6 units with the negative direction of the y-axis.
√3x − y − 6 = 0
√3x + y − 6 = 0
√3x + y + 6 = 0
-√3x + y − 6 = 0
Question 10
Given points A(2, 3) and B(5, -1), find the equation of the line that is perpendicular to the line passing through these points and passes through the midpoint of segment AB.
y = (3/4)x - 8/13
y = (3/4)x - 3/8
y = (3/4)x - 13/8
y = (4/3)x - 13/8
There are 10 questions to complete.