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Find the equartion of the line in vector...

Find the equartion of the line in vector form passing through the point ( 4 , -2,5) and parrallel to the vector `3 hat(i) + hat(j) + 2 hat(k)`.

Text Solution

Verified by Experts

The correct Answer is:
` bar r = ( 4 hati - 2 hatj + 5 hatk ) + lamda ( 3hati - hatj + 2 hatk ) `
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Find the vector equation of the line which passes through the point (3,4,5) and is parallel the vector 2 hat(i) + 2 hat(j) - 3 hat(k) .

Find the vector equation of a line passing through the point (2,3,2) and parallel to the line : vec(r) = (-2 hat(i) + 3 hat(j) ) + lambda (2 hat(i) - 3 hat(j) + 6 hat(k)) . Also, find the distnace between these two lines.

Knowledge Check

  • Find the vector equation of the line which passes through the point (3,4,5) and is parallel the vector 2 hat(i) + 2 hat(j) - 3 hat(k) .

    A
    `vec(r) = (3 hati + 4 hatj + 5 hatk ) + lambda (2 hati - 2 hatj - 3 hatk)`
    B
    `vec(r) = (3 hati + 4 hatj + 5 hatk ) + lambda (2 hati + 2 hatj - 3 hatk)`
    C
    `vec(r) = (3 hati - 4 hatj + 5 hatk ) + lambda (2 hati + 2 hatj - 3 hatk)`
    D
    `vec(r) = (3 hati + 4 hatj + 5 hatk ) + lambda (5 hati + 2 hatj - 3 hatk)`

  • The distance of the point having position vector -hat(i) + 2hat(j) + 6hat(k) from the straight line passing through the point (2, 3, –4) and parallel to the vector, 6hat(i) + 3hat(j) -4hat(k) is:

    A
    6
    B
    `4sqrt3`
    C
    `2sqrt13`
    D
    7

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    (A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

    Find the vector equation of a line through the point (5, 2, -4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8hatk ?

    Find the vector and cartesan equation of the plane passing through the poin (1,2,-4) and parallel to the lines. vec(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda (2 hat(i) + 3 hat(j) + 6 hat(k)) and vec(r) = hat(i) - 3 hat(j) + 5 hat(k) + mu (hat(i) + hat(j) - hat(k)) .

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