8. Let 1 2 +--+- () -- () ---(3) (:). at = and = 3 4 7 b3 (a) Find conditions on b₁,b2, b3 such that € span{a}, až, a}}. (b) Find a vector = (b₁,b2, b3)™ such that & span{a}, až, až}.

Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: 39. For each condition, find unit vectors å and b or explain why no such vectors exist. (a) |a+헤-0…

A:

Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

A:

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Give instructions, in detail, for how you would add, subtract, multiply, and divide: 24 and Details…

A:

Q: 19. For two non – zero vectors ā' and b,if ||a' + || = ||a'||, then which of the following is…

A: Given : For two non-zero vectors a→ and b→,  ||a→+b→||=||a→|| Use the property ||a→||2=a→.a→

Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

A:

Q: Obtain Vector v = 3î+ 4ftransformed with -1 1 3 2 –4]

A:

Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

A:

Q: Q3/A/ If ā = i – 2j + k , Find: i) (ā x b). (ā x c) ii) (ā × 5) × (ā x c) tho vectors 2i - i+ 2k and…

A:

Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

A:

Q: Find the length of the vector x = [-2, 2, 6 ]

A:

Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: :) What is a 2b2+|a.b|²? Let a = 0 and b = -2 0 2 be two vectors.

A:

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

A:

Q: Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

A:

Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions

Q: 17) Let a = [3, -4] and b = [−6, k]. a) Determine the value(s) of k such that a + b = a + 6. What is…

A:

Q: Q1// Determine äxb if å=3i-5 j+7k and b=2i-6j+4k and check if resultant vector are perpendicular to…

A: Given,           a→=3i-5j+7k and b→=2i-6j+4kTo find: a→ × b→

Q: 6. Show that the vectors (1,1,0), (1, 0, 1), and (0,1,1) generate F3.

A: In this question, we will show that the given vectors generate F3 .

Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

A:

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

A:

Q: 4. Determine whether the vector (4, 20, 2) is in the span of {(1,3,0), (0, 4, 1)). (Ex- plain your…

A: Given: .To Do:Determine whether is in the span of .

Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

A: We have to find