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Find the value of alphatimes(betatimesga...

Find the value of `alphatimes(betatimesgamma)`, where `alpha=2hat(i)-10hat(j)+2hat(k), beta=3hat(i)+hat(j)+2hat(k), gamma=2hat(i)+hat(j)+3hat(k)`.

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Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

Find 'lambda' if the vectors : hat(i)-hat(j)+hat(k), 3hat(i)+hat(j)+2hat(k) and hat(i)+lambda hat(j)-3hat(k) are coplanar.

Knowledge Check

  • The points 7hat(i)-11hat(j)+hat(k),5hat(i)+3hat(j)-2hat(k)and12hat(i)-8hat(j)-hat(k) forms

    A
    `"equilateral "Delta`
    B
    `"isosceles "Delta`
    C
    `"right angled "Delta`
    D
    collinear

  • If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

    A
    `4`
    B
    `3`
    C
    `6`
    D
    `2`

  • Area of rhombus is ......., where diagonals are a=2hat(i)-3hat(j)+5hat(k) and b=-hat(i)+hat(j)+hat(k)

    A
    `sqrt(21.5)`
    B
    `sqrt(31.5)`
    C
    `sqrt(28.5)`
    D
    `sqrt(38.5)`

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    vec(r )=(hat(i) +hat(j)) +lambda(2hat(i) -hat(j) +hat(k)) vec(r )=(2hat(i) +hat(j) -hat(k)) + mu (3hat(i) -5hat(j) +2hat(k))

    Show that the vectors hat(i)-3hat(j)+4hat(k),2hat(i)-hat(j)+2hat(k)and 4hat(i)-7hat(j)+10hat(k) are coplanar.

    vec(r ) =(6hat(i) +3hat(k) ) + lambda(2hat(i) -hat(j) +4hat(k)) vec(r )=(-9hat(i) +hat(j) -10hat(k)) + mu (4hat(i) +hat(j) +6hat(k))

    Area of rhombus is ......., where diagonals are a=2hat(i)-3hat(j)+5hat(k) and b=-hat(i)+hat(j)+hat(k)

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

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