Explanation Given information: The vectors, v = − 2 i + 2 j and w = − 3 i + 2 j Explanation: Two vectors are parallel when the angle θ between v and w is 0 or π and are orthogonal if and only if v ⋅ w = 0 . The vectors are v = − 2 i + 2 j and w = − 3 i + 2 j First find dot product of v and w . The dot product v ⋅ w is defined as the vector v ⋅ w = a 1 a 2 + b 1 b 2 , where v = a 1 i + b 1 j and w = a 2 i + b 2 j are two nonzero vectors in space. ⇒ v ⋅ w = ( − 2 i + 2 j ) ( − 3 i + 2 j ) Use the formula for a dot product, v ⋅ w = a 1 a 2 + b 1 b 2 . = ( − 2 ) ( − 3 ) + ( 2 ) ( 2 ) = 6 + 4 = 10 ⇒ v ⋅ w = 10 The dot product of v and w is not zero implies that the given vectors v and w are not orthogonal. Now to decide whether vectors v and w are parallel or not, Angle θ between two nonzero vectors v and w is defined by the formula, cos θ = v ⋅ w | | v | | | | w | | . Now to find the magnitude of each vector, The magnitude of v is defined by | | v | | = a 1 2 + b 1 2 where v = a 1 i + b 1 j

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Author: Michael Sullivan

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Chapter 9, Problem 51RE

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Whether the vectors v and w are parallel, orthogonal, or neither, where v=− 2i+2j and w=−3i+2j.

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Chapter 9, Problem 50RE

Chapter 9, Problem 52RE

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Whether the vectors v and w are parallel, orthogonal, or neither, where v = − 2 i + 2 j and w = − 3 i + 2 j .

Solution Summary: The author explains that two vectors are parallel, orthogonal, or neither, where v=-2i+2j is 0 or pi. The dot product

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Whether the vectors v and w are parallel, orthogonal, or neither, where v=− 2i+2j and w=−3i+2j.

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