If P → + Q → = R → and P + Q = R , what is the angle P → and Q → ?

As Given |P| = |Q| = |R| From vector's Formula, Now, Substituting the values, Let |P| = |Q| = |R| = x [ Only in Magnitude ] &there4; The Angle Between P & Q is 120°

If P → + Q → = R → and P + Q = R , what is the angle P → and Q → ?

As Given |P| = |Q| = |R| From vector's Formula, Now, Substituting the values, Let |P| = |Q| = |R| = x [ Only in Magnitude ] &there4; The Angle Between P & Q is 120°

Find the angle between A → = 2 i ^ + 4 j ^ + 4 k ^ and B → = 4 i ^ + 2 j ^ - 4 k ^

Given, A → = 2 i ^ + 4 j ^ + 4 k ^ B → = 4 i ^ + 2 j ^ - 4 k ^ Dot product of two vectors is given by A → . B → = ( 2 i ^ + 4 j ^ + 4 k ^ ) . ( 4 i ^ + 2 j ^ - 4 k ^ ) = 8 + 8 + 16 = 32 Magnitude of A → and B → is given by A → = 2 2 + 4 2 + 4 2 = 4 + 16 + 16 = 36 = 6 B → = 4 2 + 2 2 + ( - 4 ) 2 = 16 + 4 + 16 = 36 = 6 Therefore, angle between the two vectors is given by cos θ = A → . B → A → B → = 32 6 × 6 = 32 36 ⇒ cos θ = 0 . 88 ⇒ θ = 28 . 4 ∘

A triangle is formed by vectors a → , b → and c → = a → + b → . Prove a sin A = b sin B = c sin C

In ΔABC, Let BC= a,CA= b and AB= c, then a = B C , b = C A a n d c = A B From ΔABC, we get ⇒ B C → + C A → = B A → ⇒ B C → + C A → + A B → = 0 ⇒ a → + b → + c → = 0 ⇒ a → × ( a → + b → + c → ) = a → × 0 → ⇒ a → × a → + a → × b → + a → × c → = 0 ⇒ a → × b → = − a → × c → ⇒ a → × b → = c → × a → . . . . . . ( i ) Similarly, a → × b → = b → × c → . . . . . . ( i i ) From (i) and (ii), we get a → × b → = b → × c → = c → × a → a → × b → = b → × c → = c → × a → a b sin ( π − C ) = b c sin ( π − A ) = c a sin ( π − B ) a b sin C = b c sin A = c a sin B Dividing by abc throughout, we get sin C c = sin A a = sin B b ⇒ a sin A = b sin B = c sin C

Given a → = 4 i ^ + 3 j ^ , b → = 3 i ^ + 4 j ^ find the magnitudes of (i) a → (ii) b → (iii) a → + b → (iv) a → - b →

Given, a → = 4 i ^ + 3 j ^ b → = 3 i ^ + 4 j ^ a → + b → = 7 i ^ + 7 j ^ a → - b → = i ^ - j ^ (i) Magnitude of a → a → = 4 2 + 3 2 = 16 + 9 = 25 = 5 (ii) Magnitude of b → b → = 3 2 + 4 2 = 9 + 16 = 25 = 5 (iii) Magnitude of a → + b → a → + b → = 7 2 + 7 2 = 49 + 49 = 98 (iv) Magnitude of a → - b → a → - b → = 1 2 + 1 2 = 1 + 1 = 2