Class 12 Mathematics - Chapter Three Dimensional Geometry NCERT Solutions | If a line makes angles 90°, 135°
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Let direction cosines of the line be l, m, and n.
\begin{align}l = cos90^0=0\end{align}
\begin{align}m = cos135^0=-\frac{1}{\sqrt{2}}\end{align}
\begin{align}n = cos45^0=\frac{1}{\sqrt{2}}\end{align}
\begin{align}Therefore, the\; direction\; cosines\; of \;the\; line\; are\;0, -\frac{1}{\sqrt{2}}\;and\;\frac{1}{\sqrt{2}}\end{align}
More Questions From Class 12 Mathematics - Chapter Three Dimensional Geometry
- Q:-
Find the direction cosines of a line which makes equal angles with the coordinate axes.
- Q:-
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
- Q:-
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
- Q:-
The vertices of ΔABC are A (3, 5, −4), B (−1, 1, 2), and C (−5, −5, −2).
Popular Questions of Class 12 Mathematics
- Q:-
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
- Q:-
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
- Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- Q:-
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
- Q:-
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
- Q:- Evaluate the determinants
\begin{vmatrix} \mathbf{2} & \mathbf{4} \\ \mathbf{-5} & \mathbf{-1} \end{vmatrix} - Q:- Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation R in the set A = {1, 2, 3,13, 14} defined as
R = {(x, y): 3x − y = 0}
(ii) Relation R in the set N of natural numbers defined as
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y): y is divisible by x}
(iv) Relation R in the set Z of all integers defined as
R = {(x, y): x − y is as integer}
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y} - Q:- Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm - Q:-
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
- Q:- Integrals sin 2x
Recently Viewed Questions of Class 12 Mathematics
- Q:-
Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.
- Q:-
Represent graphically a displacement of 40 km, 30° east of north.
- Q:-
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
- Q:- \begin{align} \int sec x . \left(sec x + tan x\right) .dx \end{align}
- Q:- Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = { (a,b) ; |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
- Q:- Find the principal value of \begin{align} cosec^{-1}\left({-\sqrt2}\right)\end{align}
- Q:- Find the principal value of \begin{align} cos^{-1}\left(\frac{\sqrt3}{2}\right)\end{align}
- Q:-
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
- Q:-
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
- Q:-
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
- All Chapters Of Class 12 Mathematics
- All Subjects Of Class 12