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Find the dot product of vectors vec(a)=2...

Find the dot product of vectors `vec(a)=2hat(i)-3hat(j)+hat(k), vec(b)=-hat(i)+3hat(j)+hat(k)`

Text Solution

Verified by Experts

`vec(a).vec(b)=-2-9+=-10`
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Explore conceptually related problems

Obtain the dot product of the vectors : vec(a)=hat(i)-hat(j)+hat(k) and vec(b)=hat(i)-hat(k) .

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

Knowledge Check

  • Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

    A
    12
    B
    30
    C
    24
    D
    56

  • 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

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

    A
    `3hat(i)-hat(j)+4hat(k)`
    B
    `-3hat(i)+hat(j)+4hat(k)`
    C
    `3hat(i)+hat(j)-4hat(k)`
    D
    `-3hat(i)-hat(j)+4hat(k)`

    • Similar Questions

    Explore conceptually related problems

    Find the scalar and vector products of two vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)) and vec(b)(hat(i)-2hat(j)+3hat(k)) .

    Find the unit vector in the direction of the sum of the vectors : vec(a) = 2hat(i)-hat(j)+2hat(k) and vec(b)=-hat(i)+hat(j)+3hat(k) .

    Find the volume of the parallelepiped whose edges are represented by the vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)), vec(b)=(hat(i)+2hat(j)-hat(k)) and vec(c)=(3hat(i)-hat(j)+2hat(k)) .

    Find the volume of the parallelepiped whose coterminous edges are represented by the vectors vec(a)=2hat(i)-3hat(j)+hat(k),vec(b)=hat(i)-hat(j)+2hat(k) and vec(c)=2hat(i)+hat(j)-hat(k) .

    Find the volume of the parallelepiped whose coterminous edges are represented by the vectors (i) vec(a)=hat(i)+hat(j)+hat(k), vec(b)=hat(i)-hat(j)+hat(k), vec(c)=hat(i)+2hat(j)-hat(k) (ii) vec(a)=-3hat(i)+7hat(j)+5hat(k), vec(b)=-5hat(i)+7hat(j)-3hat(k), vec(c)= 7 hat(i)-5hat(j)-3hat(k) (iii) vec(a)=hat(i)-2hat(j)+3hat(k), vec(b)=2hat(i)+hat(j)-hat(k), vec(c)=hat(j)+hat(k) (iv) vec(a)=6hat(i), vec(b)=2hat(j), vec(c)=5hat(i)

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