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1. Given a = i-jtk, b = ai + 3j tk, p = 1 · Solve the equations a. v=p, a x v=b for v. 3. u, v, w, we have 2. Show that for any vectors i) (u± v). [(ut v) x ( u - v ) ] = 0 ii) (utv). [(uxw) x (u + v) ] = 6 If u,v,w are any vectors show that [ u x ( v x W ) ] + [ V x (wxu)] + [wx (uxv)]=0 1. Find the volume of the parallelepiped having edges or else shore that A, B, C, and D lie on a plane they lie on a find its equations. AB, AC, and AD, or on a line. If plane, find its equation; if they lie on a line. A(2,-1,3), B = (-1,2,2), (= (1,0,1), D= (4,1-1) 2. Compute (uxv) xw directly U=2; 13j-k, V = i-as +k, w = ~ i tj tak 3. Find the equation of the line through the given point and perpendicular to the given line and intersecting it. (2,-1,3); X11 = 1-2 = 2+1 3 4. Express (txu) x (vxw) in terms of v and w t = i tj - 2k, u = 3; -j tak, v = zitaj -k, w= -itj tak

1. Given a = i-jtk, b = ai + 3j tk, p = 1 · Solve the equations a. v=p, a x v=b for v. 3. u, v, w, we have 2. Show that for any vectors i) (u± v). [(ut v) x ( u - v ) ] = 0 ii) (utv). [(uxw) x (u + v) ] = 6 If u,v,w are any vectors show that [ u x ( v x W ) ] + [ V x (wxu)] + [wx (uxv)]=0 1. Find the volume of the parallelepiped having edges or else shore that A, B, C, and D lie on a plane they lie on a find its equations. AB, AC, and AD, or on a line. If plane, find its equation; if they lie on a line. A(2,-1,3), B = (-1,2,2), (= (1,0,1), D= (4,1-1) 2. Compute (uxv) xw directly U=2; 13j-k, V = i-as +k, w = ~ i tj tak 3. Find the equation of the line through the given point and perpendicular to the given line and intersecting it. (2,-1,3); X11 = 1-2 = 2+1 3 4. Express (txu) x (vxw) in terms of v and w t = i tj - 2k, u = 3; -j tak, v = zitaj -k, w= -itj tak

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Given a = i-jtk, b = ai + 3j tk, p = 1 · Solve the equations a. v=p, a x v=b for v. 3. u, v, w, we have 2. Show that for any vectors i) (u± v). [(ut v) x ( u - v ) ] = 0 ii) (utv). [(uxw) x (u + v) ] = 6 If u,v,w are any vectors show that [ u x ( v x W ) ] + [ V x (wxu)] + [wx (uxv)]=0
Transcribed Image Text:1. Given a = i-jtk, b = ai + 3j tk, p = 1 · Solve the equations a. v=p, a x v=b for v. 3. u, v, w, we have 2. Show that for any vectors i) (u± v). [(ut v) x ( u - v ) ] = 0 ii) (utv). [(uxw) x (u + v) ] = 6 If u,v,w are any vectors show that [ u x ( v x W ) ] + [ V x (wxu)] + [wx (uxv)]=0
1. Find the volume of the parallelepiped having edges or else shore that A, B, C, and D lie on a plane they lie on a find its equations. AB, AC, and AD, or on a line. If plane, find its equation; if they lie on a line. A(2,-1,3), B = (-1,2,2), (= (1,0,1), D= (4,1-1) 2. Compute (uxv) xw directly U=2; 13j-k, V = i-as +k, w = ~ i tj tak 3. Find the equation of the line through the given point and perpendicular to the given line and intersecting it. (2,-1,3); X11 = 1-2 = 2+1 3 4. Express (txu) x (vxw) in terms of v and w t = i tj - 2k, u = 3; -j tak, v = zitaj -k, w= -itj tak
Transcribed Image Text:1. Find the volume of the parallelepiped having edges or else shore that A, B, C, and D lie on a plane they lie on a find its equations. AB, AC, and AD, or on a line. If plane, find its equation; if they lie on a line. A(2,-1,3), B = (-1,2,2), (= (1,0,1), D= (4,1-1) 2. Compute (uxv) xw directly U=2; 13j-k, V = i-as +k, w = ~ i tj tak 3. Find the equation of the line through the given point and perpendicular to the given line and intersecting it. (2,-1,3); X11 = 1-2 = 2+1 3 4. Express (txu) x (vxw) in terms of v and w t = i tj - 2k, u = 3; -j tak, v = zitaj -k, w= -itj tak
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