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If the unit vectors $a with not stretchy bar on top$ and $b with not stretchy bar on top$ are inclined at an angle $2 theta$ such that $vertical line a with not stretchy bar on top minus b with not stretchy bar on top vertical line less than 1$ , then $theta$ lies in the interval

$[0, \frac{π}{6})$
$(5 \frac{π}{6}, π]$
$[\frac{π}{6}, \frac{π}{2}]$
$[\frac{π}{2}, \frac{5 π}{6}]$

hint Hint:

We are given the angle between two unit vectors. It is 2θ. We are given one condition. We have to find the interval in which θ lies.

The correct answer is: $open square brackets 0 comma pi over 6 close parentheses space$

The given condition is $open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar less than 1$
$a with rightwards arrow on top$ and $b with rightwards arrow on top$ are unit vectors.
| $a with rightwards arrow on top$ | = 1
| $b with rightwards arrow on top$ | = 1
2θ is the angle between two given vectors.
The dot product of the given vectors is given as below.
$a with rightwards arrow on top. b with rightwards arrow on top space equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar cos 2 theta space space space space space space space space space equals left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis space cos 2 theta space space space space space space space space space equals cos 2 theta$
Now, we will use the given condition to solve further.
$open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar less than 1$
$square root of open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses. open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses end root space less than space 1 square root of open vertical bar a with rightwards arrow on top close vertical bar squared space plus space open vertical bar b with rightwards arrow on top close vertical bar squared minus space 2 stack a. b space with rightwards arrow on top end root space less than 1 square root of 1 space plus space 1 space minus 2 cos 2 theta end root space less than 1 space space space space space space space space space... F r o m left parenthesis 1 right parenthesis square root of 2 left parenthesis 1 space minus space cos 2 theta right parenthesis end root space less than space 1 square root of 2 left parenthesis 2 sin squared theta right parenthesis end root space less than space 1 space space space space space space space space space space space space space... space left parenthesis space space F o r m u l a space o f space cos 2 x right parenthesis square root of 4 sin squared theta end root space less than space 1 space space space space space space 2 sin theta space less than space 1 space space space space space space space sin theta space less than space 1 half$
We know that
$sin pi over 6 space equals 1 half S o comma space w e space w a n t space v a l u e space o f space theta space s u c h space t h a t theta space less than space pi over 6 sin theta space equals space left square bracket space 0 comma 1 right square bracket A n d comma space sin 0 space equals space 0 S o comma space t h e space i n t e r v a l space o f space theta space w i l l space b e space space theta space equals left square bracket 0 comma space pi over 6 right parenthesis$
This is the final answer.

For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.

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For such questions, we should know the formulas related to homogeneous equation. Before solving the equation, we have to see if the given function is a homegenous function. A homegenous function has same degree for all its terms.

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If the unit vectors $a with not stretchy bar on top$ and $b with not stretchy bar on top$ are inclined at an angle $2 theta$ such that $vertical line a with not stretchy bar on top minus b with not stretchy bar on top vertical line less than 1$ , then $theta$ lies in the interval

$[0, \frac{π}{6})$
$(5 \frac{π}{6}, π]$
$[\frac{π}{6}, \frac{π}{2}]$
$[\frac{π}{2}, \frac{5 π}{6}]$

We are given the angle between two unit vectors. It is 2θ. We are given one condition. We have to find the interval in which θ lies.

The correct answer is: $open square brackets 0 comma pi over 6 close parentheses space$

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If the unit vectors and are inclined at an angle such that , then lies in the interval

We are given the angle between two unit vectors. It is 2θ. We are given one condition. We have to find the interval in which θ lies.

The correct answer is:

The given condition is and are unit vectors.|| = 1|| = 12θ is the angle between two given vectors.The dot product of the given vectors is given as below. Now, we will use the given condition to solve further.We know that This is the final answer.

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If the unit vectors $a with not stretchy bar on top$ and $b with not stretchy bar on top$ are inclined at an angle $2 theta$ such that $vertical line a with not stretchy bar on top minus b with not stretchy bar on top vertical line less than 1$ , then $theta$ lies in the interval

The correct answer is: $open square brackets 0 comma pi over 6 close parentheses space$

A planet moving along an elliptical orbit is closest to the sun at a distance r_¹ and farthest away at a distance of r₂. If v₁ and v₂ are the liner velocities at these points respectively, then the ratio $v subscript 1 over v subscript 2$ is

A planet moving along an elliptical orbit is closest to the sun at a distance r_¹ and farthest away at a distance of r₂. If v₁ and v₂ are the liner velocities at these points respectively, then the ratio $v subscript 1 over v subscript 2$ is

Three blocks having equal mass of $2 text end text k g$ are hanging on a string passing over a pulley as shown in figure. whal will be the tension prodoced in a string connccting the blocks B and C.

Three blocks having equal mass of $2 text end text k g$ are hanging on a string passing over a pulley as shown in figure. whal will be the tension prodoced in a string connccting the blocks B and C.

$A blank$ body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is if the body is pulled by a force P as shown in figure the limiting function between body and surface will be

$A blank$ body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is if the body is pulled by a force P as shown in figure the limiting function between body and surface will be

If the surfaces shown in figure are frictionless, the ratio of $T subscript 1 end subscript$ and $T subscript 2 end subscript$ is

If the surfaces shown in figure are frictionless, the ratio of $T subscript 1 end subscript$ and $T subscript 2 end subscript$ is

Three forces are acting simultaneously on a particle mowing with velocity $stack V with rightwards arrow on top$ . These forces are represcaled in magnitude and dircction by the three sidcs of a triangle $A B C$ . The particle will now move with velocity…..

Three forces are acting simultaneously on a particle mowing with velocity $stack V with rightwards arrow on top$ . These forces are represcaled in magnitude and dircction by the three sidcs of a triangle $A B C$ . The particle will now move with velocity…..

A body of 2 kg has an initial speed 5 m/s. A force act $c o s$ it for some time in the directive of motion. The force $left parenthesis stack F with rightwards arrow on top right parenthesis$ -me time (t) graph is shown in figure. The final speed of the body is

A body of 2 kg has an initial speed 5 m/s. A force act $c o s$ it for some time in the directive of motion. The force $left parenthesis stack F with rightwards arrow on top right parenthesis$ -me time (t) graph is shown in figure. The final speed of the body is