Right-hand rule for a × ba × b के लिए दाएँ हाथ का नियमa × b ke liye right-hand rule

NCERT Fig 10.23 · Class 12 Maths · Chapter 10 · interactive diagram

Parts and what they mean

• First vector \vec{a} (पहला सदिश \vec{a}) — Fingers start pointing along \vec{a}.
• Second vector \vec{b} (दूसरा सदिश \vec{b}) — Fingers curl from \vec{a} towards \vec{b} through the smaller angle θ.
• Unit normal \hat{n} — the direction of \vec{a} \times \vec{b} (मात्रक अभिलंब \hat{n} — \vec{a} \times \vec{b} की दिशा) — The thumb points this way, perpendicular to the plane of \vec{a} and \vec{b}. For \vec{b} \times \vec{a} it flips: -\hat{n}.
• Curl of the right-hand fingers (दाएँ हाथ की उँगलियों का घुमाव) — Like turning a screw: rotating \vec{a} into \vec{b} drives it along \hat{n}. With x → y the screw moves along +z: \hat{i} \times \hat{j} = \hat{k}.
• Angle θ (0 ≤ θ ≤ π) (कोण θ (0 ≤ θ ≤ π)) — |\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|\sin\theta.
• Plane containing \vec{a} and \vec{b} (\vec{a} और \vec{b} वाला तल) — \vec{a} \times \vec{b} is perpendicular to this whole plane.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.23. Report a mistake