Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Vector Arithmetic
Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.
Vector Calculus
Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.
Question

Transcribed Image Text:If a 3i-j-4k, b= -2i + 4j-3k and c i+ 2j -k.
Find unit vector parallel to 3 a -2 b +4 c.
Q.2 Find the vector whose magnitude is 5 and which is in the direction
of the vector 4i- 3j + k.
For what value of m, the vector 4i + 2j - 3k and mi -j+ 3k
have same magnitude?
Given the points A (1, 2, -1), B (-3, 1, 2) and C (0, -4, 3)
(i) find AB, BC, AC
Q.5 Find the lengths of the sides of a triangle, whose vertices are
A (2, 4, -1), B (4, 5, 1), C (3, 6, -3) and show that the
triangle is right angled.
Q.1
Q.3
Q.4
(ii) Show that AB+ BC AC
%3D
Q.6 If vectors 3i + j - k and 2 i - 4j + 4k are parallel, find the value
of A.
27
Q.7
Show that the vectors 4i - 6j + 9k and-6i + 9j -k are parallel.
Q.8
Find real numbers x, y and z such that
(a)
(b)
7xi + (y-3)j + 6k = 10i + 8j - 3zk
(x + 4)i + (y-5)j+(z-1)k 0
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