Here we use simple vector dot product and cross product basic rules and formulas. For dot product i.i=j.j=k.k=1 but
i.j=j.k=k.i=0
We also use formula like
(AXB) XC =(A.C)B-(B.C)A
Ax(BXC) =(A. C) B- (A. B) C
If A = 21-j-k. B=2i-Sj-k, C = j + k, find (A-B)C. A(B-C), (AxB)-C, A.(B ×...
a=4i + k Calculate the vector product axb Check that a x b is normal to a and to b Calculate exd and lexd Find a unit vector normal to the plane of the vectors b and d b- 2i-3j-k d--i+2j+k
1. Given the following 3 vectors, evaluate a. 2A+B b. C-A c. 2BXC-omit d. C-(AXB) - Ort A = 2i - 13 + 4k B=4i + ij - 5k C = -2i+2j – 3k = 120 at 450 - 200 at 1260 Find D E 2. The position of an object is related to time by X = Ata--Bt + C, where A -6m/s?.
Question 5 Find the unit vector perpendicular to each of the vectors 2i-j + k and 3计4f-k, where i,j, k are the mutually perpendicular unit vectors. Calculate the sine of the angle between the two vectors.
question about linear algebra
21. The following two lines := -i+j+ k + t(2i - 2j - 2k), t e R r and y2 1 = 2 -1 intersect each other. What is the equation of the line (where s E R) passing through the intersection point of these two lines and perpendicular to both of them? r -ijk s(i - j - k) (a) (b) r i2j+3k + s(i - 2j + 7k) (c) (d) rsik) (e) =j-k s(i...
Find the following expressions if a = 2i – 5k, b = i+j - 3k, and c = 4i + 8j + 2k. 1. a. b 2. a.C= 3. b.c=
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]
Two vectors p and q are given by: p = 2i + j - K q = i - 3j + 2k Find: a) p + q b) Modulus (p + q) c) Modulus (p) + Modulus (q) d) (p) x (q)
1)
2)
Use the vectors u = 2i - j, v = 21 - 3j, and w = -3i + 5j to evaluate the expression. 2v - u + w Find a unit vector in the same direction as the given vector. a = 201 - 21j
Let the two vectors A=4i+5j+3k,B=-2i+3j-4k, and C=3i-5j+k find: A. S= A+3 B+6C B. (-5A .B).3C C. (3B*2A)+C D. Find the angle a between A and C Let the two vectors A=4i+5j+3k,B=-2i+3j-4k, and C=3i-5j+k find: A. S= A+3 B+6C B. (-5A .B).3C C. (3B*2A)+C D. Find the angle a between A and C
Let →a=2→i−5→j−2→ka→=2i→-5j→-2k→ and →b=5→i−→kb→=5i→-k→. Find
−→a+→b-a→+b→.
Let ā = 27 – 53 – 2k and 7 = 57 - K. Find - ã+ 7. <3i Х 5j k X>