find a vector c such that that megnitude is equal to A and direction is equal to B. A=2i-j+3k. B=I+j+2k
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Answer:
ELet,
a⃗ =2i^+2j^−2k^
b⃗ =5i^+yj^+k^
c⃗ =−i^+2j^+2k^
If a⃗ ,b⃗ ,c⃗ are coplanar, then their scalar triple product should be zero.
[a⃗ b⃗ c⃗ ]=0
That implies,
(a⃗ ×b⃗ ).c⃗ =0
By cyclic rotation,
(c⃗ ×a⃗ ).b⃗ =0
We have,
c⃗ ×a⃗ =6j^−6k^
Therefore,
(6j^−6k^).(5i^+yj^+k^)=0
6y−6=0
y=1
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Czaee Shefali Kolekar
Czaee Shefali Kolekar, studied BMM at St. Xavier's College Mumbai
Answered Apr 22, 2015
let a=2i+2j-2k, b=5i+yj+k and c=-i+2j+2k
If a,b and c are coplanar, then
[a b c]=0 i.e. scalar triple product=0
=> (a x b) . c=0
or (c x a) . b=0
we have,
c x a = 6j-6k
therefore, (6j-6k).(5i+yj+k)=0
=>6y-6=0
=>y=1xplanation: