Three points P,Q,R respectively have position vectors: OP = i +j+2k OQ = 2i – j+k OR = 3i + 2j – 3k a) Find the modulus of OP and of 0Q, and the scalar product OP · 0Q. Hence find the angle between OP and 0Q. b) Find PQ, PR and QR.

Q: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: For vectors i : onto v. and w = calculate the scalar projection of w %3D comp;w (Give an answer…

A: scalar projection of w on v is =v.w|v||w|compvw¯=…

Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

A:

Q: snip

A:

Q: Given that A=2i+j-k, B=4i+2j+ck, find the scalar c such that: 1- A & B are orthogonal 2- A & B are…

A:

Q: Find the angle between u and v, also find the scalar component of u in the direction of v and the…

A: The solution to the given question is given below

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: b) Consider the vectors a = 3i - 2j+7 K, and b = -5i +4j-3k, find 1-a.b 2- Angle between a and b. 3-…

A:

Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OÁ = 2i + 5k,…

A: (a) Given that position Vectors, OA→=2i+5kOB→=3i+2j+3kOC→=i+j+k   As we know that, two vectors are…

Q: ors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are mutuallyperpendicular unit vectors…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

A:

Q: Find the angle between u and v, also find the scalar component of u in the direction of v and the…

A:

Q: Given the vector u 2i + 1j, find the - magnitude and angle in which the vector points (measured…

A:

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the angle between u and v, also find the scalar component of u in the direction of v and the…

A:

Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

A:

Q: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

A:

Q: Find the angle between the vectors u = 2i − 3j + k, v = i − 2j + k (a) in radians and (b) in…

A:

Q: 15. Given the vector u (2i + 5j) and vector v = (3i + 4j), find the dot product u v %3D

A: We have to find the dot product of given vectors.

Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: Let v = -5i + 2j and w = 2i - 4j.Find the specified vector scalar, or angle 3v - 4w.

A: It is given that, v = -5i + 2j and w = 2i - 4j

Q: Answer either A or B. A) Let V = 21 + 3j – k and W = -i - 5j – 6k, then find cos 0, where 0 is the…

A: Vector problem....

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

A:

Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: For a vector of my oriented at 245 degrees on the hexagonal system, find the projections of this…

A: We have to find the projection of a vector.

Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

A:

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

A:

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A:

Q: The.vectors (2i - 3 j) , (3i – j) and (2k - i) are Parallel to each other Perpendicular to each…

A:

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

Q: A, B and C are points in space relative to 0 such that AB 1 CO and AC 1 BO. Prove that BC 1 AO. The…

A: Given: A, B and C are points in space relative to O such that AB⊥CO and AC⊥BO. To show: BC⊥AO.…

Q: Find the angle between the vectors u = 3i + 2j + k, v = 2i − 3j (a) in radians and (b) in degrees.

A: Vector: u=3i+2j+k v=2i-3j u=<3,2,1> v=<2,-3,0>

Q: The value of A for which the vectors 2i- 4j + Ak and 3i- 6j + k parallel are

A: Given the two vectors Let's say v1 and v2 v1= 2i-4j+lemdak v2= 3i-6j+k

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

A:

Q: Given the vector A= 5ax +3ay -7az and B= 3ax +6ay-2az, find (a) a unit vector in the direction of…

A:

Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A:

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

A:

Q: Assign AB//FG, BD//GI, DE//IJ, EA//JF. and C, H are the intersections of the diagonals of the…

A: Given: Using the scalar product of the three vectors, calculate the volume of a given solid figure.

Q: Find the angle between the vectors i – k and 4i + 4j -2k

A:

Q: Determine a unit vector perpendicular to the both vectors A - 5i + 6j – 8k and B : - 2i + 5k. |0| =…

A:

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.