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 directionof the vector 4i- 3j + k.For what value of m, the vector 4i + 2j - 3k and mi -j+ 3khave same magnitude?Given the points A (1, 2, -1), B (-3, 1, 2) and C (0, -4, 3)(i) find AB, BC, ACQ.5 Find the lengths of the sides of a triangle, whose vertices areA (2, 4, -1), B (4, 5, 1), C (3, 6, -3) and show that thetriangle is right angled.Q.1Q.3Q.4(ii) Show that AB+ BC AC%3DQ.6 If vectors 3i + j - k and 2 i - 4j + 4k are parallel, find the valueof A.27Q.7Show that the vectors 4i - 6j + 9k and-6i + 9j -k are parallel.Q.8Find 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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Answered: Q.1 If a = 3i - j-4k, b= -2i + 4j- 3k…

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Q.1 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 .

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 Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

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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