Advertisements
Advertisements
प्रश्न
Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.
Advertisements
उत्तर
We have `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and `vecr * (hati - hatj + hatk)` = 5.
Solving these two equations
We get `[(2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk)]*(hati - hatj + hatk)` = 5
Which gives `lambda` = 0
Therefore, the point of intersection of line and the plane is (2, 1, 2) − and the other given point is (– 1, – 5, – 10).
Hence the distance between these two points is `sqrt([2 - (-1)^2] + [-1 + 5]^2 + [2 - (-10)]^2`
i.e. 13
APPEARS IN
संबंधित प्रश्न
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)
Find the distance between the following pairs of points:
(2, –1, 3) and (–2, 1, 3)
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 a right angled triangle.
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.
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:
A(4, –3, –1), B(5, –7, 6) and C(3, 1, –8)
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).
Determine the points in yz-plane and 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.
The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, –6) respectively, find the coordinates of the point C.
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
The distance of a point P(a, b, c) from x-axis is ______.
Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`
Find the distance of a point (2, 4, –1) from the line `(x + 5)/1 = (y + 3)/4 = (z - 6)/(-9)`
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 ______.
