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What is a unit vector ?...

What is a unit vector ?

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### Step-by-Step Solution: 1. **Definition of a Unit Vector**: A unit vector is defined as a vector that has a magnitude of exactly 1. This means that it represents only the direction of the vector without any consideration for its length. 2. **Examples of Unit Vectors**: - The unit vector in the direction of the x-axis is represented as **î** (i cap). Its magnitude is 1. - Similarly, the unit vector in the direction of the y-axis is represented as **ĵ** (j cap), and the unit vector in the direction of the z-axis is represented as **k̂** (k cap). Both of these also have a magnitude of 1. ...
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Knowledge Check

  • What is the unit vector perpendicular to the following vectors 2hati+2hatj-hatk and 6hati-3hatj+2hatk

    A
    `(hati+10hatj-18k)/(5sqrt(17))`
    B
    `(hati-10hatj+18hatk)/(5sqrt(17))`
    C
    `(hati-10hatj-18hatk)/(5sqrt(17))`
    D
    `(hati+10hatj+18hatk)/(5sqrt(17))`

  • What is the unit vector perpendicular to the following vectors 2 hat(i) + 2 hat(j) - hat(k) and 6 hat(i) - 3 hat(j) + 2 hat(k)

    A
    `(i + 10 j - 18 k)/(5 sqrt(17))`
    B
    `(i - 10 j + 18 k)/(5 sqrt(17))`
    C
    `(i - 10 j - 18 k)/(5 sqrt(17))`
    D
    `(i + 10 j + 18 k)/(5 sqrt(17))`

  • What is the unit vector perpendicular to the following Vector 2hat(i)+2hat(j)-hat(k) and 6hat(i)-3hat(j)+2hat(k)?

    A
    `(hat(i)+10hat(j)-18hat(k))/(5sqrt(17))`
    B
    `(hat(i)-10hat(j)+18hat(k))/(5sqrt(17))`
    C
    `(hat(i)-10hat(j)-18hat(k))/(5sqrt(17))`
    D
    `(hat(i)+10hat(j)+18hat(k))/(5sqrt(17))`

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