Two nonzero vectors are parallel if they point in the same direction or in opposite directions. This means that if two vectors are parallel, one must be a scalar multiple of the other. Determine whether the given vectors u and v are parallel. If they are, express v as a scalar multiple of u.

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George Blue · Accepted Answer

If two vector u and v are parallel then we can represent vector u as scalar multiple of vector u that means v=λu where λ is scalar a) Here given vector u=&amp;lt;3,−2,4&amp;gt; and v=&amp;lt;−6,4,−8&amp;gt; v=&amp;lt;−6,4,−8≥−2&amp;lt;3,−2,4&amp;gt; v=−2u - vector v is scalar multiple of vector u So given two vectors are parallel b) Here given vector u=&amp;lt;−9,−6,12&amp;gt; and v=&amp;lt;12,8,−16&amp;gt; u=&amp;lt;−9,−6,12≥3&amp;lt;−3,−2,4&amp;gt; 13u=&amp;lt;−3,−2,4&amp;gt; v=&amp;lt;12,8,−16≥−4&amp;lt;−3,−2,4&amp;gt; v=&amp;lt;12,8,−16≥−4⋅13u v=−43u vector v is scalar multiple of vector u So given two vectors are parallel c) Here given vector u=i+j+k and v=2i+2j−2k Here the two vectors cannot be represented by scalar multuiple. So the vectors are not parallel.

Two nonzero vectors are parallel if they point in the same direction o

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