सदिशों `hat(i)+4hat(j)-2hat(k)` और `3hat(i)-5hat(j)+hat(k)` के परिणामी कि दिशा में एकांक सदिश ज्ञात कीजिए |

Options

A. ` 4/(sqrt(19)) hat(i) - 1/(sqrt(19)) hat(j)+ 1/(sqrt(19)) hat(k)`
B. ` 4/(sqrt(18)) hat(i) + 4/(sqrt(18)) hat(j)+ 2/(sqrt(18)) hat(k)`
C. ` 4/(sqrt(18)) hat(i) - 1/(sqrt(18)) hat(j)- 1/(sqrt(18)) hat(k)`
D. `- 1/(sqrt(18)) hat(i) - 1/(sqrt(18)) hat(j)- 1/(sqrt(18)) hat(k)`

Answer

C

Explanation

मानलो `vec(A) =hat(i) + 4hat(j) -2 hat(k)` तथा `vec(B) = 3hat(i) - 5 hat(j) +hat(k) `
` :. vec(R) = vec(A) +vec(B)`
` = (hat(i) +4hat(j) -2hat(k)) + (3 hat(i) -5hat(j) +hat (k))`
` = (1+3) hat(i) +(4-5) hat(j) +(-2 +1) hat(k)`
` = 4 hat(i) - hat(j) -hat(k)`
` :. vec(R) ` कि दिशा में एकांक सदिश ` hat(R) = (vec(R))/(|vec(R)|)`
` = (4hat(i) -hat(j) -hat(k))/(sqrt(4^(2)+(-1)^(2)+(-1)^(2))) = (4 hat(i) -hat(j)-hat(k))/(sqrt(18))`
` = 4/(sqrt(18)) hat(i) - 1/(sqrt(18)) hat(j)- 1/(sqrt(18)) hat(k)`