If A =4 hat i -3 hat j and B =5 hat i -18 hat j then magnitude and direction of A + B will be:

Question

If A =4 hat i -3 hat j and B =5 hat i -18 hat j then magnitude and direction of A + B will be: (A) 17.49 , tan-1 (2) (B) 15 , tan-1 (4/3) (C) 20 , tan-1(4/5) (D) 17.49 , tan-1 (5/3)

Tardigrade Admin · Accepted Answer

| A + B |=4 hat i -3 hat j +5 hat i +18 hat j =9 hat i +15 hat j | A + B |=√(9)2+(15)2 =√81+225=√306=17.49 tan θ=(15/9)=(5/3) ⇒ θ= tan -1((5/3))

Q. If $A = 4 \hat{i} - 3 \hat{j}$ and $B = 5 \hat{i} - 18 \hat{j}$ then magnitude and direction of $A + B$ will be:

$17.49, t a n^{- 1}$ (2)

$15, t a n^{- 1} (4/3)$

$20, t a n^{- 1}$ (4/5)

$17.49, t a n^{- 1} (5/3)$

$∣ A + B ∣ = 4 \hat{i} - 3 \hat{j} + 5 \hat{i} + 18 \hat{j}$

$= 9 \hat{i} + 15 \hat{j}$
$∣ A + B ∣ = (9)^{2} + (15)^{2}$

$= 81 + 225 = 306 = 17.49$
$tan θ = \frac{15}{9} = \frac{5}{3}$

$\Rightarrow θ = tan^{- 1} (\frac{5}{3})$

Q. If A=4i^−3j^​ and B=5i^−18j^​ then magnitude and direction of A+B will be:

17.49,tan−1 (2)

15,tan−1(4/3)

20,tan−1(4/5)

17.49,tan−1(5/3)