Question

If the three vectors 2i-j +k

Answer 1

Let,

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....

happy rakhsha bandhan...