Question

1. Carefully draw the line segment PQ that connects P=(4, 5, -3) $sdPFzg86RyCVCPGa6QAAAABJRU5ErkJggg==$ and Q=(0, -4, 2) $QEgZTwp09NxKwAAAABJRU5ErkJggg==$ . Include dotted vertical lines from the xy-plane to P and Q to show perspective.

2. Find the distance between P and Q, from the previous problem. Then find the coordinates of the midpoint of the line segment PQ .

3. Let u= -3i+5j+7k $SN3L3QTIAAAAASUVORK5CYII=$    and v= 10i+j-2k $8e53Wdq4idgAAAABJRU5ErkJggg==$ . Show that u × v $0z8VCYumUAjg+yPQzwAAAAASUVORK5CYII=$ is orthogonal to the vector v $e3mzn3Ub30fDoxzeu+IAAAAASUVORK5CYII=$ .

Answer 1

Griven pointi porus, -3) 0 (0, -4,2) p(4,5,-3) 2 - - - 4 co, -4,2) to y a de 4 22 Dritance between ple. pand o is given by pluis,-3), 010-4, 2) - AxJ" + (4,-405"+(21-21) 114-6) + (5+41+ (-3-2} 16+ 81 + 25 a po's ll.our co ordinater og Mid point q po. (rithe, eithr ett Mid point ( uto 54, 342) : (2,0.5, -0.5)

Mid point q po is r 2, 0.5, -0.5) 2 I Ginen valon u -3it sit ak (x, if y, jf Zik) 1. v. 1oit j - 2K (neity, jf zok). - ū xüli La determinant کے 12 Y کے Z

. (5x-2 - 981) -(-57-2 - 7x10) +k(-3X1 - 5x10) ,(-10-1) -;16-20) 4x4-3-50) I uxū a -laitbuj - s3k ? uxu is orthogonal to ū To Delemine whether Find clot product ( Dot product of laob, aboso orthogonal vection is zero] if 0-90 aboo) (lux ū ). 5). (12 i +6uj - 534)•(10i + j-26) : 1173(10) + (64)61 +-53)-2) .-170 +64 + 106 Hence Uxu is orthogant to t]