{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# vctut01 - (b Find the magnitudes of the velocity and...

This preview shows page 1. Sign up to view the full content.

The University of Sydney School of Mathematics and Statistics Tutorial 1 MATH2061: Vector Calculus Summer School 2012 1. Let u = 3 i j k , v = i + 3 j + k and w = 2 i 3 k . Find ( u · v ) w , u ( v · w ) , ( u × v ) · w , u · ( v × w ) , ( u × v ) × w , u × ( v × w ) . 2. Find the equations of the straight lines that satisfy each of the following sets of conditions. Give answers in vector form, parametric scalar form and Cartesian form. (a) The line passes through the points P ( 2 , 1 , 3) and Q (1 , 4 , 2) . (b) The line passes through the point P (1 , 2 , 4) and is parallel to the line given by r = ( i + j + 6 k ) + (4 i j + k ) t. (c) The line passes through the point P (0 , 1 , 3) and is perpendicular to the plane 4 x 3 y + z = 7. 3. A particle moves along a curve whose parametric equations are x ( t ) = sin t, y ( t ) = te t , z ( t ) = cos t, where t is the time. (a) Determine its velocity vector and acceleration vector.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (b) Find the magnitudes of the velocity and acceleration at t = 0 . 4. Describe geometrically the vector ±elds determined by each of the following vector functions: (a) F = − 2 i + 3 j ; (b) F = x i + y j . 5. Evaluate i C F · d r , where F = z i + x j + y k and r ( t ) = t i + t 2 j + 3 k ; t : 0 → 1. 6. Calculate the work done by the force ±eld F = 2 i − 3 xy j in moving from A : (0 , , 0) to B : (2 , 4 , 0) (a) along the straight line AB ; (b) along the straight lines from A to D : (2 , , 0) and then from D to B ; (c) along the piece of the parabola y = x 2 , z = 0 from A to B . Copyright c c 2012 The University of Sydney...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online