IIT JEE , AIEEE Forum - Mathematics , Vectors

monur3

Q.1 [a*p b*q c*r] + [a*q b*r c*p] + [a*r b*p c*q] =

1)3 2)1 3)-3 4)0

Q.2 a=i+j+k and r is a variable vector such that r.i,r.j,r.k are positive integers. if r.a<=12then number of values of is

a)12C9 -4 b)12C9 c)12C4 d)none.

karthik_abiram

a*p is (a . p) or (a x p)?

monur3

sorry i should have mentioned it.

All the * signs means cross product.

Greatdreams

Reply to quesn 2

r = xi + yj + zk

r is a vector and a is the another vector

r.a

12

So the number of values of r = No of +ve integral

solutions of

( x+y+z

12 )

= _{[n = 3 ]}

^{[12] n- 1}C ₂ = ² C ₂ + ³ C ₂ +............+¹¹ C ₂

Now since ⁿ C_r = ⁿ C _n-r

So we have³C ₀+ ³C₁ + ⁴C₂ +......+¹¹C₉

=⁴C₁ + ⁴C₂ +.....+ ¹¹C₉ = ¹² C ₉

Hence option B is correct.

Hope it helps.....Sorry for not being able to put the

vector signs.Nudge if not clear.Rate if satisfied.

karthik_abiram

[a*p b*q c*r] + [a*q b*r c*p] + [a*r b*p c*q] =

i think sum info may have been given abt the nature of a,b,c and abt p,q,r........lik not zero vectors,not parallel vectors.......etc..........

if not consider the special case,like a=0 and the answer will be ZERO

if the answer is mentioned sumthing else,plz do mention me.......

Cheers!

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