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Compute the magnitude of the following v...

Compute the magnitude of the following vectors
`vec(a)=hat(i)+hat(j)+hat(k),vec(b)=2hat(i)-7hat(j)-3hat(k)`
and `vec(c)=(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k)`.

Text Solution

Verified by Experts

The correct Answer is:
`|vec(a)|=sqrt(3),|vec(b)|=sqrt(62),|vec(c)|=1`
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Find the angle between the vectors vec(a)=3hat(i)+2hat(j)-hat(k),vec(b)=-2hat(i)-3hat(j)+hat(k) .

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Knowledge Check

  • If vec(a)=hat(i)+2hat(j)+hat(k),vec(b)=2hat(i)-2hat(j)+2hat(k) and vec(c)=-hat(i)+2hat(j)+hat(k) , then

    A
    `vec(a)` and `vec(b)` have the same directions
    B
    `vec(a)` and `vec(c)` have opposite directions
    C
    `vec(b)` and `vec(c )` have opposite directions
    D
    no pair of vectors have same directions

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    Find the sum of the vectors vec(a) = hat(i) - 2hat(j) + hat(k), vec(b) = -2hat(i) + 4hat(j) + 5hat(k) and vec(c) = hat(i) - 6hat(j) - 7hat(k) .

    Find angle theta between the vectors vec(a) = hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

    Find [vec(a)vec(b)vec(c )] , if vec(a)=hat(i)-2hat(j)+3hat(k),vec(b)=2hat(i)-3hat(j)+hat(k) and vec(c )=3hat(i)+hat(j)-2hat(k) .

    Determine k such that a vector vec(r) is at right angles to each of the vectors vec(a) = k hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - k hat(k) and vec(c) = -2hat(i) + k hat(j) + 3hat(k) .

    Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

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    Find the magnitude of vec(a) given by vec(a) = (hat(i) + 3hat(j) - 2hat(k)) xx (-hat(i) + 3hat(k)) .

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