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What is the area of the triangle OAB whe...

What is the area of the triangle OAB where O is the origin, `vec(OA)=3hat(i)-hat(j)+hat(k) and vec(OB)=2hat(i)-hat(j)+3hat(k)` ?

Text Solution

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The correct Answer is:
`(1)/(2)5sqrt(6)` sq. units.
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Find a unit vector in the direction of (vec(a)+vec(b)) , where : vec(a)=2hat(i)+2hat(j)-5hat(k) and vec(b)=2hat(i)+hat(j)+3hat(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) .

Knowledge Check

  • What is the area of Delta OAB , where O is the origin, OA= 3 hat(i) - hat(j) + hat(k) and OB= 2 hat(i) + hat(j)- 3hat(k) ?

    A
    A) `5 sqrt6` sq units
    B
    B) `(5 sqrt6)/(2)` sq units
    C
    C) `sqrt6` sq units
    D
    D) `sqrt30` sq units

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

    A
    Parallel
    B
    Antiparallel
    C
    Perpendicular
    D
    at acute angle with each other

  • The area of the triangle whose adjacent sides are : vec(a)=3hat(i)+hat(j)+4hat(k) and vec(b)=hat(i)-hat(j)+hat(k) is :

    A
    `(1)/(2)sqrt(42)`
    B
    42
    C
    `sqrt(42)`
    D
    `sqrt(21)`

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    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).

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    Determine a vector product of vec(A)=hat(i)+hat(j)+hat(k)and vec(B)=-3hat(i)+hat(j)+hat(k)

    If G is the centroid of the triangle PQR, where vec(GP)=2hat(i)+hat(j)+3hat(k),vec(GQ)=hat(i)-hat(j)+2hat(k), then the area of the triangle PQR is

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