Direction cosines of the line through two pointsदो बिंदुओं से जाने वाली रेखा की दिक्-कोसाइनDo points se jaane wali line ke direction cosines

NCERT Fig 11.2 · Class 12 Maths · Chapter 11 · interactive diagram

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Parts and what they mean

x-axis (OX) (x-अक्ष (OX)) — One of the three mutually perpendicular axes; here it comes out of the page towards you.
y-axis (OY) (y-अक्ष (OY)) — The second axis, drawn to the right.
z-axis (OZ) (z-अक्ष (OZ)) — The third axis, pointing straight up.
Origin O(0, 0, 0) (मूल बिंदु O(0, 0, 0)) — The point where the three axes meet.
P(x₁, y₁, z₁) (P(x₁, y₁, z₁)) — The first given point.
Q(x₂, y₂, z₂) (Q(x₂, y₂, z₂)) — The second given point.
R — foot of the perpendicular from P (R — P से डाले गए लंब का पाद) — P dropped straight down to the XY-plane.
S — foot of the perpendicular from Q (S — Q से डाले गए लंब का पाद) — Q dropped straight down to the XY-plane.
N — foot of the perpendicular from P on QS (N — P से QS पर लंब का पाद) — N is at the height of P on the vertical line QS, so NQ = z_2 - z_1.
PR ⟂ XY-plane (PR ⟂ XY-तल) — Vertical segment; its length is z_1.
QS ⟂ XY-plane (QS ⟂ XY-तल) — Vertical segment; its length is z_2.
RS in the XY-plane (XY-तल में RS) — Shadow of PQ on the floor (XY-plane).
PN ⟂ QS (PN ⟂ QS) — Horizontal segment at the height of P.
NQ = z₂ − z₁ (NQ = z₂ − z₁) — How much higher Q is than P.
Line PQ (रेखा PQ) — The only line through P and Q; its length is PQ = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.
Right triangle PNQ (समकोण त्रिभुज PNQ) — Right angle at N; the angle at Q is γ.
γ = ∠PQN (γ = ∠PQN) — Angle of PQ with the vertical (z-direction); \cos\gamma = \dfrac{z_2-z_1}{PQ}.
cos γ from the triangle (त्रिभुज से cos γ) — Adjacent side NQ over hypotenuse PQ. In the same way \cos\alpha = \dfrac{x_2-x_1}{PQ}, \cos\beta = \dfrac{y_2-y_1}{PQ}.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.2. Report a mistake