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Find a unit vector perpendicular to both...

Find a unit vector perpendicular to both the vectors `(2hat(i)+3hat(j)+hat(k))` and `(hat(i)-hat(j)-2hat(k))`.

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To find a unit vector that is perpendicular to both vectors \( \mathbf{A} = 2\hat{i} + 3\hat{j} + \hat{k} \) and \( \mathbf{B} = \hat{i} - \hat{j} - 2\hat{k} \), we can use the cross product of the two vectors. The cross product of two vectors results in a vector that is perpendicular to both. ### Step-by-Step Solution: 1. **Identify the vectors**: \[ \mathbf{A} = 2\hat{i} + 3\hat{j} + \hat{k} \] ...
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Find a unit vector perpendicular to each of the vectors hat(i)+2hat(j)-3hat(k) and hat(i)-2hat(j)+hat(k) .

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Knowledge Check

  • A unit vector perpendicular to each of the vectors 2hat(i) - hat(j) + hat(k ) and 3hat(i) - 4hat(i) - hat(k) is

    A
    `(1)/(sqrt3) hat(i) + (1)/(sqrt3) hat(j) - (1)/(sqrt3) hat(k)`
    B
    `(1)/(sqrt2) hat(i) + (1)/(2) hat(j) + (1)/(2) hat(k)`
    C
    `(1)/(sqrt3) hat(i) - (1)/(sqrt3) hat(j) -(1)/(sqrt3) hat(k)`
    D
    `(1)/(sqrt3) hat(i) + (1)/(3) hat(j) + (1)/(sqrt3) hat(k)`

  • 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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    Find a unit vector perpendicular to the plane of two vectors a=hat(i)-hat(j)+2hat(k) and b=2hat(i)+3hat(j)-hat(k) .

    Find a vector of magnitude 15, which is perpendicular to both the vectors (4hat(i) -hat(j)+8hat(k)) and (-hat(j)+hat(k)).

    Find a vector of magnitude 7 units, which is perpendicular to two vectors : 2hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) .

    Find a vector perpendicular to vector vec(A)=(hat(i)+2hat(j)-3hat(k)) as well as vec(B)=(hat(i)+hat(j)-hat(k))

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