2) Express the resultant vector as a linear combination of unit vectors i and j and find the magnitude and direction angle. u = 57 + 77 and = -31 + 37; Find -5u + 2v two xectors.

Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

A:

Q: B) Determine if the two vectors are orthogonal or parallel or not? A=6i + 6k and B--2i +2j+2k

A: We have to check that the two vectors A→ and B→ are orthogonal or parallel. So, we find the angle…

Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: In a standard coordinate system, the unit vectors in the three main directions are orthogonal to…

A:

Q: Express the given vector in terms of the unit vectors i, j, and k. (2, -5, 0)

A:

Q: Write three properties of parallel vectors p and q.

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b,…

A: Given that P , Q & R lie on a straight line. It means vectors are coplanar . since if vectors…

Q: Find two unit vectors parallel to v = -2i + 5j – 3k.

A: Given:- v=-2i +5j-3k  To find:- Two units vectors parallel to given vector v

Q: Find the angle between two vectors, 6 and 8 units long, when their resultant is (a) 10 units long…

A: Given: The angle between two vectors, 6 and 8 units long

Q: Express the vector in terms of the unit vectors i and j. 4) (4,

A:

Q: Show steps clearly.

A:

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C = ix - iy + iz Find the following:…

A:

Q: Find the angle between two vectors by using cross product (V,xV2) V, = 3i + 9j + 6k V2 = i + 3j + 2k…

A:

Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: Which two vectors are perpendicular to both a and b?

A:

Q: Find the unit vector in the same direction as v = 2i - 3j -6k

A: Given vector is v=2i-3j-6k. To find the unit vector in the same direction of the given vector.…

Q: Find the unit vector that has the same direction as the vector v = 3i - 2j.

A: Given vector is v→=3i-2j We have to find unit vector that has same direction as given vector.…

Q: Find the unit vector having the same direction as v. v = 3i - 4j 3. 4 3 Ou-15i-20j

A: We have to find unit vector

Q: Determine the angle, to the nearest degree, between the vectors= (4,6,-2) and y = (1,8,2)

A: Solution is done in step 2

Q: What is the unit vector with the same direction as the vector v = 2i - 7j? Write as a linear…

A:

Q: The vector from the origin to point A is given as 6a, – 2a, – 4a., and the unit vector directed from…

A: The vector from the origin to point A is 6ax-2ay-4az Therefore, vector A is A→=6,-2,-4 Now, the unit…

Q: Find the unit vector that has the same direction as the vector v = 8i - 6j.

A: Given vectorv=8i^-6j^

Q: 2. If å and b are two vectors with lengths 2 and 5 and angles between 150°, respectively, obtain the…

A:

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

A:

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: Find the unit vector having the same direction as v. v= - 3i + 4j

A:

Q: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

Q: Find the angle O between the vectorS 3. and -2

A: Given: 34-2 &114 We can write given vectors as, u=3, 4, -2v=1, 1, 4 We know that,…

Q: Express the vectors in terms of their lengths anddirections. √2i + √2j

A: If a vector is defined as: v→=ai+bj Then, the length or magnitude of the vector is: |v→|=a2+b2 The…

Q: Find the position vector of the point of intersection of the line joining the points whose position…

A: Given: The position vector of the points 5i^-4j^ and -3i^+4j^; -13i^+4j^ and -5i^+j^

Q: Which two vectors are perpendicular to both å and b?

A: result of vector cross product of two vector is perpendicular to both the vectors.

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: 10,7 and -2,-75

Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: Find the angle a between the vectors 3 2 B [B] and -4 -3

A:

Q: Given a vector v with initial point P(5,12) and terminal point Q(−2,−12), write the vector in terms…

A: vector with initial p1,p2 and                 terminal (q1,q2)is given by v=<q1-p1,q2-p2>

Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

Q: Express the vectors in terms of their lengths anddirections. i + 2j - k

A: Given:  i + 2j - k

Q: The angle between vector A =4ax+5ay+6az and B = 3ax -2ay + 4az is * O 68.75 degrees O 56.62 degrees…

A: Angle between two vectors

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: Determine the angle, to the nearest degree, between the vectors = (5,3), b= (-1,–2)

A:

Q: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

A:

Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…