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    1. Two vectors are parallel provided that one is a scalar multiple of the other. Determine whether the vectors a and b are parallel, perpendicular, or neither.

    a = 12i - 20j + 17k and b = -9i + 15j + 24k

    2. Find a unit vector n perpendicular to the plane through the points P(1, 3, -2), Q(2, 4, 5), and R(-3, -2, 2). Then find the distance from the origin to this plane by computing n ? OP.

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    Solution Preview

    a ⃗∙b ⃗=|a ⃗ ||b ⃗ |Cosϑ

    a ⃗∙b ⃗=(12i - 20j + 17k)∙(-9i + 15j + 24k)=-108-300+408=0

    Since,a ⃗∙b ⃗=0,therefore,|a ⃗ ||b ⃗ |Cosϑ is also equal to zero.
    |a ⃗ |≠0
    |b ⃗ ...

    Solution Summary

    This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Vectors and provides students with a clear perspective of the underlying concepts.