if a and b are unit vectors inclined at an angle theta

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If unit vectors vec A and vec B are inclined at an angle theta ,Then

Click here👆to get an answer to your question ✍️ If unit vectors vec A and vec B are inclined at an angle theta ,Then | vec A - vec B | is .

If unit vectors

Question A and B

are inclined at an angle θ,Then

∣ ∣ ∣ ∣ ​ A − B ∣ ∣ ∣ ∣ ​ is .

A2sin

2 θ ​

B2cos

2 θ ​

C2tan

2 θ ​

D

tan θ

Medium Open in App

Updated on : 2022-09-05

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Correct option is A)

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If unit vectors  and B̂ are inclined at an angle θ, then

If unit vectors  and B̂ are inclined at an angle θ, then | B̂| is equal to

Byju's Answer Standard XII Physics Unit Vectors If unit vecto... Question If unit vectors ^ A and ^ B

are inclined at an angle

θ , then | ^ A − ^ B | is equal to A 2 cos θ 2 B sin θ C 2 sin θ 2 D cos θ Open in App Solution

The correct option is D

2 sin θ 2 We can write, | ^ A − ^ B | 2 = | ^ A | 2 + | ^ B | 2 − 2 | ^ A | | ^ B | cos θ ⇒ | ^ A − ^ B | 2 = 1 + 1 − 2 cos θ ⇒ | ^ A − ^ B | 2 = 2 ( 1 − cos θ ) ⇒ | ^ A − ^ B | 2 = 4 sin 2 θ 2 ( ∵ 1 − cos θ = 2 sin 2 θ 2 ) ⇒ | ^ A − ^ B | = 2 sin θ 2 Suggest Corrections 14

SIMILAR QUESTIONS

Q.

Let two non-collinear unit vectors

^ a and ^ b

form an acute angle. A point P moves so that at any time t the position vector

→ O P

(where, O is the origin) is given by

^ a cos t + ^ b sin t

. When P is farthest from origin O, let M be the length of

→ O P and ^ u

be the unit vector along

→ O P . Then,

Q.

Let ^ a , ^ b a n d ^ c

be three unit vectors such that

^ a × ( ^ b × ^ c ) = √ 3 2 ( ^ b + ^ c ) . If ^ b is not parallel to ^ c

, then the angle between

^ a and ^ b is

Q. If

^ a , ^ b and ^ c

are unit vectors satisfying

| ^ a − ^ b | 2 + | ^ b − ^ c | 2 + | ^ c − ^ a | 2 = 9 , then | 2 ^ a + 5 ^ b + 5 ^ c | is

Q. Let

^ a , ^ b , ^ c

are three unit vectors such that

^ a + ^ b + ^ c

is also a unit vector. If pairwise angles between

^ a , ^ b , ^ c are θ 1 , θ 2 and θ 3 respectively then cos θ 1 + cos θ 2 + cos θ 3 equals?

Q. If three unit vector

^ a , ^ b , ^ c satisfy ^ a + ^ b + ^ c = ^ 0

, then the angle between

^ a and ^ b is View More EXPLORE MORE Unit Vectors

Standard XII Physics

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If vec(a) and vec(b) are unit vectors inclined at an angle theta, then prove that sin""(theta)/(2) = (1)/(2)

If vec(a) and vec(b) are unit vectors inclined at an angle theta, then prove that sin""(theta)/(2) = (1)/(2)|hat(a) - hat(b)|.

Home > English > Class 12 > Maths > Chapter > Vector Algebra >

If vec(a) and vec(b) are unit ...

If a ⃗ a→ and b ⃗ b→

are unit vectors inclined at an angle

θ θ , then prove that sin θ 2 = 1 2 ∣ ∣ a ˆ − b ˆ ∣ ∣ sinθ2=12|a^-b^| .

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Updated On: 27-06-2022

Text Solution Answer

The correct Answer is

1 2 ∣ ∣ a ˆ − b ˆ ∣ ∣ 12|a^-b^| Answer

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