1. Consider the following vector, (-1, 1).(a) Find two unit vectors parallel to 7.(b) Find a vector of magnitude 7 in the opposite direction of T.2. Are the vectors, =i+j+k and d=2i+3j- k, parallel, orthogonal, or neither?

Given,v=-i^+j^a) Find unit vector parallel to v.We know…

Answered: 1. Consider the following vector, T =…

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. Consider the following vector, (-1, 1).
(a) Find two unit vectors parallel to 7.
(b) Find a vector of magnitude 7 in the opposite direction of T.
2. Are the vectors, =i+j+k and d=2i+3j- k, parallel, orthogonal, or neither?

Expert Solution

Step 1

$G i v e n, v = - \hat{i} + \hat{j} a) F i n d u n i t v e c t o r p a r a l l e l t o v . W e k n o w t h a t \hat{v} = \frac{v}{|v|} \hat{v} = \frac{- \hat{i} + \hat{j}}{\sqrt{{(- 1)}^{2} + 1^{2}}} \hat{v} = \frac{- \hat{i} + \hat{j}}{\sqrt{1 + 1}} \hat{v} = \frac{- \hat{i} + \hat{j}}{\sqrt{2}} \hat{v} = - \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} . b) F i n d v e c t o r o f m a g n i t u d e 7 i n t h e o p p o s i t e d i r e c t i o n o f v . \to v e c t o r o f m a g n i t u d e 7 i n t h e o p p o s i t e d i r e c t i o n o f v i s - 7 \hat{v} T h a t i s - 7 \hat{v} = - 7 (- \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}) - 7 \hat{v} = \frac{7}{\sqrt{2}} \hat{i} - \frac{7}{\sqrt{2}} \hat{j} . 2) A r e v e c t o r, v = \hat{i} + \hat{j} + \hat{k} a n d u = 2 \hat{i} + 3 \hat{j} - \hat{k} a r e p a r a l l e l, o r t h o g o n a l o r n o r ? I f t w o v e c t o r s a r e p a r a l l e l t o e a c h o t h e r t h e n t h e y a r e s c a l a r m u l t i p l e o f e a c h o t h e r, h e r e, v a n d u a r e n o t s c a l a r m u l t i p l e o f e a e o t h e r . I f t w o v e c t o r s a r e p e r p e n d i c u l a r t o e a c h o t h e r t h e n t h e i r d o t p r o d u c t i s z e r o . H e r e, v . u = (\hat{i} + \hat{j} + \hat{k}) . (2 \hat{i} + 3 \hat{j} - \hat{k}), v . u = 2 + 3 - 1, v . u = 4 \neq 0 T h e r e f o r e, v a n d u n o t o r t h o g o n a l, T h e r e f o r e v a n d u n e i t h e r p a r a l l e l n o r o r t h o g o n a l .$