Winter 2008 - Chan's Class - Exam 1

Winter 2008 - Chan's Class - Exam 1 - Math 20C Winter 2008...

This preview shows pages 1–3. Sign up to view the full content.

Jan 30, 2008 Math 20C Winter 2008 M IDTERM 1( A ) Solutions 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. The following three space vectors are all parallel to the same plane which is this very sheet of paper: ±w ±v ±u where the vectors ±v and ±w are parallel to each other. For problems (i) – (vi) below, state whether the given object is: (a) the number zero, (b) the zero vector, (c) a nonzero vector perpendicular to the page, (d) a nonzero vector parallel to the page, (e) none of the above or undeﬁned. No justiﬁcation required. Each choice might appear more than once. (i) proj ±w ±v (d). The projection of any vector onto a vector ±w is always either a vector parallel to ±w , or the zero vector. Since ±v is neither zero nor perpendicular to ±w , its projection to ±w must be parallel to ±w , in particular to this page. (ii) ( ±w × ±u ) · ±v (a). ±w × ±u is perpendicular to the page because ±u and ±w are parallel to the page and not to each other. In particular, ±w × ±u is perpendicular to ±v . (iii) ( ±v · ±w ) ±u (d). ±v · ±w is a nonzero number, for the two vectors are not perpendicular to each other. So this is a nonzero scalar multiple of ±u , which is parallel to the page. (iv) ±u × ( ±u × ±v ) (d). ±u × ±v is perpenicular to the page, and ±u × ( ±u × ±v ) is perpendicular to ±u × ±v . The answer follows from the fact that any vector perpendicular to a normal vector
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

Winter 2008 - Chan's Class - Exam 1 - Math 20C Winter 2008...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online