Advertisements
Advertisements
प्रश्न
If a line makes an angle of `pi/4` with each of y and z axis, then the angle which it makes with x-axis is ______.
Advertisements
उत्तर
If a line makes an angle of `pi/4` with each of y and z axis, then the angle which it makes with x-axis is α = `pi/2`.
Explanation:
Let it makes angle α with x-axis.
Then `cos^2alpha + cos^2 pi/4 + cos^2 pi/4` = 1
Which after simplification gives α = `pi/2`.
APPEARS IN
संबंधित प्रश्न
Name the octants in which the following points lie:
(–5, 4, 3)
Name the octants in which the following points lie:
(7, 4, –3)
Name the octants in which the following points lie:
(2, –5, –7)
Name the octants in which the following points lie:
(–7, 2 – 5)
Find the image of:
(–5, 4, –3) in the xz-plane.
Planes are drawn through the points (5, 0, 2) and (3, –2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed.
Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, –4).
Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.
If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.
Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle.
Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.
Write the distance of the point P (2, 3,5) from the xy-plane.
Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.
Write the length of the perpendicular drawn from the point P(3, 5, 12) on x-axis.
Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.
Find the point on y-axis which is at a distance of \[\sqrt{10}\] units from the point (1, 2, 3).
The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is
The coordinates of the foot of the perpendicular from a point P(6,7, 8) on x - axis are
The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is
The length of the perpendicular drawn from the point P(a, b, c) from z-axis is
If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.
Find the coordinates of the point where the line through (3, – 4, – 5) and (2, –3, 1) crosses the plane passing through three points (2, 2, 1), (3, 0, 1) and (4, –1, 0)
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
Prove that the lines x = py + q, z = ry + s and x = p′y + q′, z = r′y + s′ are perpendicular if pp′ + rr′ + 1 = 0.
Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.
If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane
Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.
Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0.
Show that the points `(hati - hatj + 3hatk)` and `3(hati + hatj + hatk)` are equidistant from the plane `vecr * (5hati + 2hatj - 7hatk) + 9` = 0 and lies on opposite side of it.
If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is ______.
The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.
The angle between the line `vecr = (5hati - hatj - 4hatk) + lambda(2hati - hatj + hatk)` and the plane `vec.(3hati - 4hatj - hatk)` + 5 = 0 is `sin^-1(5/(2sqrt(91)))`.
The angle between the planes `vecr.(2hati - 3hatj + hatk)` = 1 and `vecr.(hati - hatj)` = 4 is `cos^-1((-5)/sqrt(58))`.
