Advertisements
Advertisements
Question
Distance of the point (α, β, γ) from y-axis is ______.
Options
β
|β|
|β| + |γ|
`sqrt(alpha^2 + γ^2)`
Solution
Distance of the point (α, β, γ) from y-axis is `sqrt(a^2 + γ^2)`.
Explanation:
Required distance = `sqrt((alpha - 0)^2 + (beta - beta)^2 + (γ - 0)^2)`
= `sqrt(alpha^2 + γ^2)`
APPEARS IN
RELATED QUESTIONS
Find the distance between the pairs of points:
(2, 3, 5) and (4, 3, 1)
Find the distance between the following pairs of points:
(–3, 7, 2) and (2, 4, –1)
Find the distance between the following pairs of points:
(–1, 3, –4) and (1, –3, 4)
Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.
Verify the following:
(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.
Find the distance between the following pairs of points:
P(1, –1, 0) and Q(2, 1, 2)
Find the distance between the following pairs of point:
A(3, 2, –1) and B(–1, –1, –1).
Find the distance between the points P and Q having coordinates (–2, 3, 1) and (2, 1, 2).
Using distance formula prove that the following points are collinear:
P(0, 7, –7), Q(1, 4, –5) and R(–1, 10, –9)
Using distance formula prove that the following points are collinear:
A(3, –5, 1), B(–1, 0, 8) and C(7, –10, –6)
Determine the points in xy-plan are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).
Show that the points (0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of an isosceles right-angled triangle.
Show that the points A(1, 3, 4), B(–1, 6, 10), C(–7, 4, 7) and D(–5, 1, 1) are the vertices of a rhombus.
Prove that the tetrahedron with vertices at the points O(0, 0, 0), A(0, 1, 1), B(1, 0, 1) and C(1, 1, 0) is a regular one.
Show that the points (3, 2, 2), (–1, 4, 2), (0, 5, 6), (2, 1, 2) lie on a sphere whose centre is (1, 3, 4). Find also its radius.
If the distance between the points P(a, 2, 1) and Q (1, −1, 1) is 5 units, find the value of a.
Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, −5, 7) and (3, 0, 1).
Find the distance of the point whose position vector is `(2hati + hatj - hatk)` from the plane `vecr * (hati - 2hatj + 4hatk)` = 9
Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`
Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`
Prove that the line through A(0, –1, –1) and B(4, 5, 1) intersects the line through C(3, 9, 4) and D(– 4, 4, 4).
Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis
Find the shortest distance between the lines given by `vecr = (8 + 3lambdahati - (9 + 16lambda)hatj + (10 + 7lambda)hatk` and `vecr = 15hati + 29hatj + 5hatk + mu(3hati + 8hatj - 5hatk)`
Find the equation of the plane through the intersection of the planes `vecr * (hati + 3hatj) - 6` = 0 and `vecr * (3hati + hatj + 4hatk)` = 0, whose perpendicular distance from origin is unity.
If one of the diameters of the circle x2 + y2 – 2x – 6y + 6 = 0 is a chord of another circle 'C' whose center is at (2, 1), then its radius is ______.
The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a ______.
