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The vector equation to the line through ...

The vector equation to the line through the point (2, 3, 1) and parallel to the vector (4, -2, 3)

A

`bar(r)=(4bar(i)-2bar(j)+3bar(k))+t(2bar(i)+3bar(j)+bar(k))`

B

`bar(r)=(2bar(i)+3bar(j)+bar(k))+t(2bar(i)-5bar(j)+2bar(k))`

C

`bar(r)=(2bar(i)+3bar(j)+bar(k))+t(4bar(i)-2bar(j)+3bar(k))`

D

`bar(r)=(4bar(i)-2bar(j)+3bar(k))+t(6bar(i)+bar(j)+4bar(k))`

Text Solution

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The correct Answer is:
C
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Find the vector equation of the plane passing through the point (1, -2, 5) and parallel to the vectors (6, -5, -1), (-3, 5, 0).

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Knowledge Check

  • The vector equation of the plane passing through the point (1, 2, 3) and parallel to the vectors (-2, 3, 1), (2, -3, 4) is

    A
    r = s (2i + j - k) + t (i + 2j + 2k)
    B
    r = 2i + 2j - 3k + s (3i + 3j - 5k) + t (i + 2j + k)
    C
    r = (i + 2j + 3k) + s (-2i + 3j + k) + t (2i - 3j + 4k)
    D
    none

  • The vector equation of the plane passing through the point (1, -2, -3) and parallel to the vectors (2, -1, 3), (2, 3, -6) is

    A
    r = (i - 2j - 3k) + s(2i - j + 3k) + t(2i + 3j - 6k)
    B
    r = (1 - s - t) (i - 2j - 3k) + s(2i - j + 3k) + t(2i + 3j - 6k)
    C
    r = (i - 2j - 3k) + s(4j - 9k)
    D
    r = (4j - 9k) + s(i - 2j - 3k)

  • A : The vector equation of the line passing through the point 2i + 3j - 4k and parallel to the vector 6 + 3j - 4k is r = (2i + 3j - 4k) + t(6i + 3j - 4k). R : The vector equation of the line passing through the point a and parallel to the vector b is r = a + tb

    A
    Both A and R are true and R is the correct explanation of A.
    B
    Both A and R are ture but R is not the correct explanation of A.
    C
    A is ture, but R is false
    D
    A is false, but R is true

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