In a ΔABC, ∠A+∠B=120∘,a=3+1,b=3−1, then the ratio of ∠A to ∠B is (a) 7:1 (b) 5:1 (c) 3:1 (d) 5:3

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In a {A}{B}{C}, {A}+{B}={120}^{},{a}={{3}}+{1},{b}={{3}}-{1},

Question

In a $Δ A B C, ∠ A + ∠ B = 120^{\circ}, a = 3 + 1, b = 3 - 1$ , then the ratio of $∠ A$ to $∠ B$ is (a) $7 : 1$ (b) $5 : 1$ (c) $3 : 1$ (d) $5 : 3$

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Sebastian Discussed

In a

Δ A B C, ∠ A + ∠ B = 120^{\circ}, a = 3 + 1, b = 3 - 1

, then the ratio of

∠ A

∠ B

is (a)

7 : 1

(b)

5 : 1

(c)

3 : 1

(d)

5 : 3

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Practice questions from similar books

Question 1

Consider the set of eight vector

V = {a \hat{i} + b \hat{j} + c \hat{k}; a, b c \in {- 1, 1}} ˙

Three non-coplanar vectors can be chosen from

V

2^{p}

ways. Then

p

is_______.

View solution

Question 2

Show that the points A, B, C with position vectors

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

View solution

Question 3

Write the number of vectors of unit length perpendicular to both the vectors

a = 2 \hat{i} + \hat{j} + 2 \hat{k}

and

b = \hat{j} + \hat{k}

View solution

Question 4

Let two non-collinear unit vector

\overset{a}{^}

a n d

\hat{b}

form an acute angle. A point

P

moves so that at any time

t,

the position vector

O P (w h e r e O

is the origin

)

is given by

\overset{a}{^} cos t + \hat{b} sin t \dot{W} h e n P

is farthest from origin

O,

let

M

be the length of

O P a n d \overset{u}{^}

be the unit vector along

O P ˙

Then (a)

\overset{u}{^} = \frac{a ^ + b ^}{∣ ∣ a ^ + b ^ ∣ ∣} a n d M = (1 + \overset{a}{^} \dot{\hat{b}})^{1 / 2}

(b) \displaystyle\hat{{u}}=\frac{{\hat{{a}}-\hat{{b}}}}{{{\left|\hat{{a}}-\hat{{b}}\right|}}}{a}{n}{d}{M}={\left({1}+\hat{{a}}\dot{{\hat}}\right)}^{{{1}/{2}}}(c)

\overset{u}{^} = \frac{a ^ + b ^}{∣ ∣ a ^ + b ^ ∣ ∣} a n d M = (1 + 2 \overset{a}{^} \dot{\hat{b}})^{1 / 2}

(d)

\overset{u}{^} = \frac{a ^ - b ^}{∣ ∣ a ^ - b ^ ∣ ∣} a n d M = (1 + 2 \overset{a}{^} \dot{\hat{b}})^{1 / 2}

View solution

Question Text

In a

Δ A B C, ∠ A + ∠ B = 120^{\circ}, a = 3 + 1, b = 3 - 1

, then the ratio of

∠ A

∠ B

is (a)

7 : 1

(b)

5 : 1

(c)

3 : 1

(d)

5 : 3

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In a ΔABC, ∠A+∠B=120∘,a=3​+1,b=3​−1, then the ratio of ∠A to ∠B is (a) 7:1 (b) 5:1 (c) 3:1 (d) 5:3

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Practice questions from similar books

In a $Δ A B C, ∠ A + ∠ B = 120^{\circ}, a = 3 + 1, b = 3 - 1$ , then the ratio of $∠ A$ to $∠ B$ is (a) $7 : 1$ (b) $5 : 1$ (c) $3 : 1$ (d) $5 : 3$