IIT JEE , AIEEE Forum - Mathematics , Vectors

palak_priya

if u and v are unit vectors and

is the acute angle between them, then 2u*3v is a unit vector for

a) exactly one value of

b) exactly two values of

c) more than two values of

d) no value of

dhwanitmunshi

correct answer is (B)
u and v are unit vectors
so 2u and 3v are the same vectors but no longer unit vectors
they are vectors with magnitudes of two and three in the same direction thus the angle is still the same
so

is still the angle b/w them

rate me if u find it correct

amarnath_mahadevuni

is it the vector product between 2u and 3v in the question?

palak_priya

venkat_tatolu

2u.3v=1(since unit vector)

implies 6u.v=1

implies 6 mod(u) mod(v) cos(theta)=1 (since angle between u and v is

same as that of 2u and 3v)

implies 6 1 1 cos(theta)=1 (since u and v unit vectors)

implies cos(theta)= 1/6

so option B is correct.(since Theta belogs to either 1st or second quadrant)

gagsdon

Is the question cross product or dot product?????

sooraj

it should be in 1st or 4th quadrant

gagsdon

Maybe my answer is wrong

but still i will try, if um wrong do tell me

I think the answer is c) more than 2 values of

2u X 3v = 6 u.v Sin

= 6 sin

( since u and v are unit vectors)

for the above product to be unit vector it its magnitude should be 1

taking a constant direction, its magnitude must be 1 or -1

since sin

has 4 values( 2 for 1/6 and 2 for -1/6) in one period hence possible values of

are 4 ie more than 2

Betu

Look ..2u x 3v =6uv.sin

in the direction of perpendicular to u & v (determined by RH thumb rule..

as sin

= sin (180-

)...we have two angle

, 180-

for which whole thing will be same.. ther is no other angle between 0-360 which make the sine of that equal...

so the answer is only two..or b)

hope it helps

gagsdon

But cant the direction be opposite with the magnitude 1????

180 + and -

can also solve the purpose

Betu

no. in that case though the magnitude is same , but direction is opposite..therefore unit vector is not same .( for being same for any vector , direction and magnitude both have to be same)

prdpram08

you are giving in the question 2u*3v,i think you are saying about dot product

its formula is a*b=abcos(theta)

soit means 2u*3v=2.3cos(theta)

therefore it will be 6.cos(theta)
and we know cos(theta) ranges from 0 to 1

therefore in any case thedot product wont be a unit vector
as we have a constant here 6
so answer is

(d)
pls give me the answer for this

raymonttcherian

ans - B

solution

mod. 2u*3v= 2u.3v.sin

= 6uvsin

sin

= 1/6 for unit vector

this happens twice from 0 to 180 deg.

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