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Show that the straight lines vec(r)=(5ha...

Show that the straight lines `vec(r)=(5hat(i)+7hat(j)-3hat(k))+s(4hat(i)+4hatj-5hat(k))andvec(r)=(8hat(i)+4hat(j)+5hat(k))+t(7hat(i)+hat(j)+hat(k))` are coplanar. Find the vector equation of the plane in which they lie.

Text Solution

Verified by Experts

The correct Answer is:
`17x-47y-24z=172`
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Similar Questions

Explore conceptually related problems

Show that the lines vec(r)=(6hat(i)+hat(j)+2hat(k))+s(hat(i)+2hat(j)-3hat(k)),andvec(r)=(3hat(i)+2hat(j)-2hat(k))+t(2hat(i)+4hat(j)-5hat(k)) are skew lines and hence find the shortest distance between them.

Find the angle between the line vec(r)=(2hat(i)-hat(j)+hat(k))+t(6hat(i)+2hat(j)-2hat(k))" and the plane "vec(r)*(6hat(i)+3hat(j)+2hat(k))=8

Knowledge Check

  • The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+hat(j)-2hat(k))" and the plane "vec(r)*(hat(i)+hat(j))+4=0 is

    A
    `0^(@)`
    B
    `30^(@)`
    C
    `45^(@)`
    D
    `90^(@)`

  • The point of inersection of the line vec(r)=(hat(i)-hat(k))+t(3hat(i)+2hat(j)+7hat(k))" and the plane "vec(r)=(hat(i)+hat(j)-hat(k))=8 is

    A
    `(8,6,22)`
    B
    `(3t+1,2t,7t-1)` for some value of t
    C
    `(-8,-6,-22)`
    D
    `(x-1)/(3)=(y-0)/(2)=(z+1)/(7)=" for some value of t "`

  • If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=3hat(i)+5hat(j)-hat(k), then a vector perpendicular to vec(a) and lies in the plane containing vec(b)andvec(c) is

    A
    `-17hat(i)+21hat(j)-97hat(k)`
    B
    `17hat(i)+21hat(j)-97hat(k)`
    C
    `-17hat(i)-21hat(j)+97hat(k)`
    D
    `-17hat(i)-21hat(j)-97hat(k)`

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    Show that the vectors are coplanar hat(i)-2hat(j)+3hat(k),-2hat(i)+3hat(j)-4hat(k),-hat(j)+2hat(k)

    show that the vectors 3 hat(i)- 2hat(j)+ hat(k), hat(i)-3hat(j)+5hat(k) and 2hat(i)+ hat(j)- 4 hat(k) form a right angled triangle

    Show that four points whose position vectors are given 6hat(i)-7hat(j) ; 16hat(i)-19hat(i)-4hat(k) ; 3hat(i)-6hat(k) ; 2hat(i)-5hat(j)+10hat(k) are co-planar

    Show that the points whose position vectors are 2hat(i) + 3hat(j) - 5hat(k), 3hat(i) + hat(j) - 2hat(k) and 6hat(i) - 5hat(j) + 7hat(k) are collinear.

    Show that the vectors are coplanar 2hat(i)+3hat(j)+hat(k),hat(i)-hat(j),7hat(i)+3hat(j)+2 hat(k)

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