next up previous
Next: About this document ...

\fbox{ \parbox{16cm}{ 1) The set $x^2+y^2+ z^2-10z=9$\ is a sphere of radius \\ a) $3$\ \\ b) $\sqrt{34}$\ \\ c) $34$\ \\ }}

\fbox{ \parbox{16cm}{ 2) $\vec{v},\vec{w}$\ are vectors in space. Then $(\vec{v... ...{w} \times \vec{v})$\ is a \\ a) vector \\ b) scalar \\ c) not defined \\ }}

\fbox{ \parbox{16cm}{ 3) If $P,Q,R$\ are three points in space, then \\ a) $\ve... ...{P Q} + \vec{Q R} = \vec{0}$. \\ c) $\vec{P Q} + \vec{Q R} = \vec{R P}$. \\ }}

\fbox{ \parbox{16cm}{ 4) If ${\rm proj}_v(w) = {\rm proj}_w(v)$, then \\ a) $\v... ...orthogonal. \\ c) $\vec{v} = \lambda \vec{w}$\ for some constant $\lambda$. }}

\fbox{ \parbox{16cm}{ 5) $\vec{u} \cdot (\vec{v} \times \vec{w})$\ is \\ a) alw... ... \\ b) always positive or zero. \\ c) can be positive or negative or zero. }}

\fbox{ \parbox{16cm}{ 6) Which of the following identities is {\bf not} always t... ...$\vert\vec{v} \times \vec{w}\vert \leq \vert\vec{v}\vert + \vert\vec{w}\vert$ }}

\fbox{ \parbox{16cm}{ 7) If $\vec{v} = (1,2,3)$, $\vec{w} = (-2,-4,-6)$, then \\... ...and $\vec{w}$\ are the same. \\ c) $\vec{v}$\ and $\vec{w}$\ are orthogonal. }}

\fbox{ \parbox{16cm}{ 8) Assume $L$\ is the line $r(t) = P+t \vec{v}$\ with $P=(... ...f not} on the line? \\ a) $(4,6,8)$. \\ b) $(2,2,2)$. \\ c) $(-2,-2,-2)$. }}

\fbox{ \parbox{16cm}{ 9) If $\vec{v} = (1,2,3), \vec{w} = (2,2,-2)$, then \\ a)... ...{w}$\ have the same length. \\ c) $\vec{v}$\ and $\vec{w}$\ are orthogonal. }}

\fbox{ \parbox{16cm}{ 10) If $\vert\vec{v} + \vec{w}\vert^2 = \vert\vec{v}\vert^... ...ther orthogonal or parallel. \\ c) $\vec{v}$\ and $\vec{w}$\ are orthogonal. }}



oliver knill 2004-07-01