Find the magnitude of R → given by R → = 3 i ^ + 11 j ^ + 4 k ^ .

Magnitude of vector R → = 3 i ^ + 11 j ^ + 4 k ^ R → = ( 3 ) 2 + ( 11 ) 2 + ( 4 ) 2 = 9 + 11 + 16 = 36 = 6

Find the magnitude of R → given by R → = 3 i ^ + 11 j ^ + 4 k ^ .

Magnitude of vector R → = 3 i ^ + 11 j ^ + 4 k ^ R → = ( 3 ) 2 + ( 11 ) 2 + ( 4 ) 2 = 9 + 11 + 16 = 36 = 6

If A → + B → + C → = 0 , show that A × B → = B → × C →

Given, A → + B → + C → = 0 Pre - Multiplying B → on both sides. B → × A → + B → + C → = B → × 0 ⇒ B → × A → + B → × B → + B → × C → = 0 ⇒ - A → × B → + 0 + B → × C → = 0 ⇒ B → × C → = A → × B → Hence, proved.

The magnitude of the resultant of a → and b → is equal to that of a → and is perpendicular to a → . Show that | b → | = 2 · a .

Let R be the resultant of two vectors a → and b → R = a 2 + b 2 + 2 a b cos θ According to the question, R = a Also if R is perpendicular to the vector a → a . ( a + b ) = 0 a . a + a b cos θ = 0 a 2 + a b cos θ = 0 cos θ = - a / b Therefore, resultant equation becomes a = a 2 + b 2 + 2 a b ( - a / b ) Squaring both sides a 2 = a 2 + b 2 - 2 a 2 b 2 = 2 a 2 b = 2 a 2 Hence proved.