Q.1If a = 3i - j-4k, b= - 2i + 4j- 3k and c =i+ 2j-k.Find unit vector parallel to 3 a -2 b +4 c .Find the vector whose magnitude is 5 and which is in the directionof the vector 4i - 3j + k.Q.2For what value of m, the vector 4i + 2j - 3k and mi - j+ V3 khave same magnitude?Given the points A = (1, 2, – 1), B = (-3, 1, 2) and C = (0, -4, 3)(i) find AB, BС, АСFind 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.3Q.4(ii) Show that AB + BC = ACQ.5Q.6If vectors 3i + j - k and 2i – 4j + 4k are parallel, find the valueof 1.Q.7Show that the vectors 4i – 6j + 9k and -6i + 9j –27-k are parallel.Q.8Find real numbers x, y and z such that(а)(b)7xi + (у - 3)j + 6k %3D 10i + 8j —3zk(x +4)i + (y-5)j+ (z- 1)k = 0%3D

Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

If a = 31 - j-4k, b= - 2i + 4j- 3k and c =i+ 2j-k. Find unit vector parallel to 3 a -2 b +4 c 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+ V3 k have same magnitude?

If a = 31 - j-4k, b= - 2i + 4j- 3k and c =i+ 2j-k. Find unit vector parallel to 3 a -2 b +4 c 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+ V3 k have same magnitude?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Question

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 .
Find the vector whose magnitude is 5 and which is in the direction
of the vector 4i - 3j + k.
Q.2
For what value of m, the vector 4i + 2j - 3k and mi - j+ V3 k
have same magnitude?
Given the points A = (1, 2, – 1), B = (-3, 1, 2) and C = (0, -4, 3)
(i) find AB, BС, АС
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.3
Q.4
(ii) Show that AB + BC = AC
Q.5
Q.6
If vectors 3i + j - k and 2i – 4j + 4k are parallel, find the value
of 1.
Q.7
Show that the vectors 4i – 6j + 9k and -6i + 9j –
27
-k are parallel.
Q.8
Find real numbers x, y and z such that
(а)
(b)
7xi + (у - 3)j + 6k %3D 10i + 8j —3zk
(x +4)i + (y-5)j+ (z- 1)k = 0
%3D

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