1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa + b, find the value of A if P, Q and R lie on a straight line. 4 a + 2b,

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

A:

Q: Suppose u = (-3, 2) and v = (10, 2) are two vectors that form the sides of a parallelogram. Then the…

A:

Q: It is known that the area of the parallelogram P formed by the vectors u and V is 14 square units…

A:

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

A:

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vector A = 2i-i+3k…

A: There is no specific formula.Please go through the solution.

Q: Let A = (-3, 4), B = (-2, b), C = (1, 6), and D = (a, 2). Then AB and DC are opposite sides of the…

A:

Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: -4 Evaluate x if the vectors 2 and are: 5 a perpendicular b parallel

A: x2 & -4  5 a. Since the vectors are perpendicular, therefore their dot product is zero. That is,…

Q: a, b, c are non-zero vectors and a is perpendicular to both b and c. If |a|= 2, \b|= 3, |c|= 4 and…

A:

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b),…

A:

Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

A:

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

A:

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

A:

Q: Given the three vectors A = (3, 1, 1), B = (2, -1, 1), C = (0, 1, 2), find (AxB)xC %3D

A: The vector can be multiplied using the scalar product or dot product and vector product or cross…

Q: Suppose that u and v are vectors in R' both of length 2V2 and that the length of u-vis also?V2 Then…

A:

Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

A:

Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

A:

Q: This question relates to three vectors defined as p = j- 3k, q =-2i-j-3k and r = 4i + j+ 3k, where…

A:

Q: latél Show that if a is perpendicular to each of the vectors and then a is perpendicular to 26 +4

A: The detail solution is given below

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

A:

Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

Q: Find the sum of the given vectors; + B Å = 440 N Z 236°, B= 580 N Z 162° Draw and label a diagram…

A: Obtain the graph of vectors as follows: The third arrow is the resultant vector.

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: Two vectors ñ and m are said to be parallel if n-m-0

A: False

Q: Find the measure of the angle between the two vectors. 4) u =(-6, -2) v = (6,-6)

A: An angle between 2 vectors is defined as, cosθ=u→·v→|u→||v→|   Here given vectors are,…

Q: Two vectors ñ and m are said to be parallel if ñ-m-0

A:

Q: Find the angle between the given vectors to the nearest tenth of a degree.u = <2, -4>, v =…

A:

Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

A:

Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

A:

Q: Two vectors are defined as A = ax + 2ay + 3az and B = 3ax + 2ay -7az . Which of the following vector…

A:

Q: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: The angle between the vectors a=(2,6) and b=(3,-1) is :إختر أحد الخيارات а. 4 b. С. 3 d. 2

A: The required angle is, option (b) π/2 The detailed solution is as follows below:

Q: Suppose that u and v are vectors in R' both of length 2V2 v is also? v2. Thenllu + v|| and that the…

A:

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: For what values of a and B will the vector (a, 1, B) be orthogonal to (4, 0, 3) and (-1, 1, 2)? a =…

A:

Q: and b are two unit vectors such that + 2b and 5 a. 4 b are perpendicular to each other, then the…

A:

Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

A:

Q: For what values of a, b, and care the vectors (2a-b,a-2b,6) and (-2,2,a+b-2c) equal?

A: The given vectors are 2a-b,a-2b,6 and -2,2,a+b-2c . Note that, two vectors are equal if their…

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: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…

Q: 14. Given that a and bare two vectors, then the vector (a + b) × (a – b) is A. perpendicular to (a –…

A:

Q: Suppose that u and v are vectors in R^7 both of length 2√2 and that the length of    u − v is also…

A: Given, u=22v=22u-v=22

Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

A: