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The vectors vec(a)=(2-x)hat(i)+2 hat(j)+...

The vectors `vec(a)=(2-x)hat(i)+2 hat(j)+2hat(k)," "vec(b) = 2hat(i)+(2-y)hat(j)+2hat(k)," "vec(c)=2hat(i)+2hat(j)+(2-z)hat(k) and vec(d) = hat(i) +hat(j)+hat(k)` are coplanar, then

A

`1/x+1/y+1/z = 1`

B

`1/(1-x)+1/(1-y)+1/(1-z) = 1`

C

` x + y + z= 1`

D

` 1/(x-2)+ 1/(y-2)+ 1/(z- 2) = 1`

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A
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Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

If vec(a)=2hat(i)+3hat(j)+hat(k), vec(b)=hat(i)-2hat(j)+hat(k) and vec(c )=-3hat(i)+hat(j)+2hat(k) , find [vec(a)vec(b)vec(c )] .

Find the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

Find vec(a).(vec(b)xx vec(c )) if : vec(a)=2hat(i)+hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c )=3hat(i)+hat(j)+2hat(k) .

If vec(a)=2hat(i)+hat(j)+3hat(k),vec(b)=-hat(i)+2hat(j)+hat(k) , and vec(c)=-3hat(i)+hat(j)+2hat(k) , find [hat(a)hat(b)hat(c)] .

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