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vec(A)=2hat(i)+4hat(j)+4hat(k) and vec(B...

`vec(A)=2hat(i)+4hat(j)+4hat(k)` and `vec(B)=4hat(i)+2hat(j)-4hat(k)` are two vectors. Find the angles between them.

Text Solution

Verified by Experts

`costheta=(vec(A).vec(B))/(|vec(A)|.|vec(B)|)`
`=(a_(1) b_(1)+a_(2)b_(2)+a_(3)b_(3))/(|vec(A)|.|vec(B)|)=(2xx4+4xx2-4xx4)/(|vec(A)|.|vec(B)|)=0`
`:. theta=cos^(-1)(0^(@))rArrtheta=90^(@)`
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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).

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Knowledge Check

  • Let vec(A)=2hat(i)-3hat(j)+4hat(k) and vec(B)=4hat(i)+hat(j)+2hat(k) then |vec(A)xx vec(B)| is equal to

    A
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    B
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    D
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  • If vec(A)=-2hat(i)+3hat(j)-4hat(k)and vec(B)=3hat(i)-4hat(j)+5hat(k) then vec(A)xxvec(B) is

    A
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    B
    `-hat(i)+2hat(j)-hat(k)`
    C
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    D
    `-hat(i)-2hat(j)-hat(k)`

  • Given two vectors vec(A) = -hat(i) + 2hat(j) - 3hat(k) and vec(B) = 4hat(i) - 2hat(j) + 6hat(k) . The angle made by (A+B) with x-axis is :

    A
    `30^(@)`
    B
    `45^(@)`
    C
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