Let overset arrow a+ overset arrow b+ overset arrow c= overset arrow 0 , where overset arrow a, overset arrow b and overset arrow c are three non-zero vectors such that the angle between overset arrow a and overset arrow b is (π /3) . If the angle between overset arrow b and overset arrow c is (π /18) , then the angle between overset arrow a and overset arrow c is

Question

Let overset arrow a+ overset arrow b+ overset arrow c= overset arrow 0 , where overset arrow a, overset arrow b and overset arrow c are three non-zero vectors such that the angle between overset arrow a and overset arrow b is (π /3) . If the angle between overset arrow b and overset arrow c is (π /18) , then the angle between overset arrow a and overset arrow c is (A) (5 π /18) (B) (11 π /18) (C) (π /2) (D) (π /6)

Tardigrade Admin · Accepted Answer

From the figure, it is clear that overset arrow a, overset arrow b, overset arrow c forms a triangle <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-mkpv6u85utn8.png" /> ∴ Angle between overset arrow a overset arrow c=π -(2 π /3)-(π /18)=(5 π /18)

Q. Let $a \to + b \to + c \to = 0 \to$ , where $a \to, b \to$ and $c \to$ are three non-zero vectors such that the angle between $a \to$ and $b \to$ is $\frac{π}{3}$ . If the angle between $b \to$ and $c \to$ is $\frac{π}{18}$ , then the angle between $a \to$ and $c \to$ is

$\frac{5 π}{18}$

$\frac{11 π}{18}$

$\frac{π}{2}$

$\frac{π}{6}$

From the figure, it is clear that $a \to, b \to, c \to$ forms a triangle

$∴$ Angle between $a \to & c \to = π - \frac{2 π}{3} - \frac{π}{18} = \frac{5 π}{18}$

Q. Let a→+b→+c→=0→ , where a→,b→ and c→ are three non-zero vectors such that the angle between a→ and b→ is 3π​ . If the angle between b→ and c→ is 18π​ , then the angle between a→ and c→ is

185π​

1811π​

2π​

6π​