Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 6, Problem 40P
(a)
To determine
The angles between the given vectors.
(b)
To determine
The angles between the given vectors.
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Vectors A→A→ and B→B→ both have a magnitude of 8. If their resultant has a magnitude of 10, what is the angle between them?
1. Given vectors A = ax + 3az and B = 5ax + 2ay - 6az, Determine:
(a) A + B
(b) 5A - B
(c)The component of A along ay
(d) A unit vector parallel to 3A + B
2. Given points P(1.-3,5), Q(2,4,6), and R(0,3,8), find:
(a) The position vectors of P and R
(b) The distance vector FOR
(c) The distance between Q and R
Find the angle between each of the following pairs of vectors
(II)
(1) A 3.00i + 5.00j
(2) A = -4.00i + 2.00j
B = 10.00i + 6.00j
B = 7.00i + 14.00j
and
and
Chapter 6 Solutions
Physics for Scientists and Engineers
Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10P
Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - Prob. 48PCh. 6 - Prob. 49PCh. 6 - Prob. 50PCh. 6 - Prob. 51PCh. 6 - Prob. 52PCh. 6 - Prob. 53PCh. 6 - Prob. 54PCh. 6 - Prob. 55PCh. 6 - Prob. 56PCh. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Prob. 62PCh. 6 - Prob. 63PCh. 6 - Prob. 64PCh. 6 - Prob. 65PCh. 6 - Prob. 66PCh. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Prob. 69PCh. 6 - Prob. 70PCh. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - Prob. 73PCh. 6 - Prob. 74P
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- Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }.arrow_forwardTwo vectors P = 2i + bj + and a-i+j+k will be parallel if (d) b=- 4 (a) b = 0 (b) ь — 1 (c) b = 2arrow_forwardUse the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.arrow_forward
- Given the three vectors P = 3x + 2ŷ − 2, Q = −6x − 4ỹ + 22, R = â – 2ŷ – 2 find two that are perpendicular and two that are parallel or antiparallel.arrow_forwardThree vectors are given by a→=4.00î + (3.00)ĵ +(4.00)ka→, b→=0î +(-3.00)ĵ +(-4.00)k and c→=-3.00î +(1.00)ĵ +(4.00)k Find (a) a → (b→x c→) (b) a→·(b→+c→) (c) x- component, (d) y-component, and (e) z- component of a→x(b→+c→) respectively.arrow_forwardGiven the vectors; A = i + 2j + 3k B = 4i + 5j + 6k C = 3i+2j + k Ď= 6i + 5j + 4k 1. Find: A + B + C + D A + B - C - D A - B + C-D (A + B) x (C + D) 2. The magnitude of vectors A, B, C, D 3. The angles and basis vectors between A, B, C, D 4. Angles of A with B, C, D 5. Projection of A onto directions of B,C,D 6. Product of AXB, B×C and C × D and its angles with Darrow_forward
- Given vectors P=(3 m, 4 m) and Q=(4 m, 3 m), find the angle of P + Q.arrow_forwardif A⃗ =2i+3j+6kA→=2i+3j+6k and A⃗ =3i−4j+2kA→=3i−4j+2k, then the angle between the two vectors isarrow_forwardThree vectors →A , →B, and →C have the following x and y components: x-component y-component →A -9.00 6.00 →B 8.00 -6.50 →C 0.00 5.50 What is the magnitude of R→=A→−B→−C→ ?arrow_forward
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