The vector a has a magnitude of 7. Its x component is 2, and its y component is twice its z component. What is its y component? a) 3 O b) 4 c) 5 d) 6

Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: Pls help

A: ABC is an equilateral triangle and D E f are the midpoints of the sides

Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

A:

Q: The angle between two unit vectors e and f is π/6 . What is the length of e × f?

A: The angle between two unit vectors e and f is π6.

Q: For what value of m, the vector 4i + 2j – 3k and mi – j+ V3 k have same magnitude? Q.3

A:

Q: In the figure, a vector a→ with a magnitude of 24.1 m is directed at angle θ = 68o counterclockwise…

A: Given that: Magnitude of a→ =24.1mAngle of a→ w.r.t. coordinate axes: θ=68°Angle of primed…

Q: Consider the figure below. If AABC is translated using the vector (r, y) → (1- 3, y+3), then rotated…

A: Identify the coordinate of C: The coordinate of C is: C-4, 1

Q: Find the magnitude of the vector and the angle 6,0° <0<360°, that the vector makes with the positive…

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Q: Find the positive value of m that makes the angle between the vectors equal to 5 a = i +j+k b = mi –…

A: Given that, a⇀=i^+j^+k^ b⇀=mi^-k^ Then we get, a⇀·b⇀=i^+j^+k^·mi^-k^a⇀·b⇀=m+0-1=m-1 Moreover we get,…

Q: Find the angle between the vectors u = 2i +j+9k, v = 6i – 12j and sketch the vectors and the angle…

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Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

A:

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Suppose that the magnitude of vector u = 5 and the magnitude of vector v=7 and the dot product of u…

A:

Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: Find the direction cosines of the vector v = 2i−4j + 4k, and approximate the direction angles to the…

A: `The given vector is v=2i-4j+4k

Q: In the diagram, ABC is an equilateral triangle, and D, E and F are the midpoints of its sides. As a…

A:

Q: The angle between the vectors i + 2j + k and 3i+ j - 5k is

A: Given: Let, A=i+2j+kB=3i+j−5k

Q: Find cos 0, where 0 is the angle between two vectors a = 2i – 3j + 2k, b = -2i + 2j+6k

A:

Q: Consider a 50-N weight suspended by two wires as shown in the accompanying figure. If the magnitude…

A: Given: 50-N weight suspended by two wires.            F1=35 N

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

Q: Find the unit vector that has the same direction as v = 2i + 2j−k.

A: To find the unit vector for any vector v=ai+bj+ck, the formula v=a2+b2+c2 can be used. This formula…

Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: Given the vector equation R(t) = (4 – 3t?)i + (t³ – 3t)j, find the angle between N(1) and R"(1),

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Q: 3. Calculate the angle (degrees), between vectors p = 2i +9j – 4k and q = -3i + 5j + 6k correct to…

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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: A=\+2) -Kg B=-i+j+ K, Csitk, D= i+2j-K which vectors are: @ perpendicular parallel-

A:

Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

A:

Q: Given the two vectors A = 3ix + 4iy and B = 7ix – 24 iy a. What is their dot product? b. What is…

A: Given : A=3ix+4iy, B=7ix-24iy.

Q: For what value of m, the vector 4i + 2j – 3k and mi – j + V3 k have same magnitude?

A: Given Data: Vector 1: x1i+x2j+x3k=4i+2j-3k Vector 2: y1i+y2j+y3k=mi-j+3k The magnitude of vector 1…

Q: In the rectangular prism shown below, OA=a, OC=b and oD =c. Express each of the following vectors in…

A: We have to express sides of rectangular I  prism in terms of vector a, b, and c

Q: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

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Q: Which vector has the smaller magnitude: u = 3i - j - k or v = 2(i + j + k)?

A: Our Aim is to tell which vector given below has the smaller magnitude u⇀=3i-j-k and v⇀=2i+2j+2k.

Q: B side of cube = 10 cm (A. B); (C. D); (E.G);(G.B) ? (Ex F); (A x G) dan (Cx F) ? 2. what is the…

A: From the given figure we get A→ = 10i+10k B→ =10iC→ =5j+10kD→=5i +10kE→ =10i+10jF→=10kG→=10i+10j+10k…

Q: Based on the table below that showcases the value of u and v can you find a vector [h k] that is not…

A:

Q: The unit vector in the direction of E=6i+8j is 0.3i+4j F

A:

Q: Given the vector u = - 6i – 3j, find the magnitude and angle in which the vector points (measured…

A: Here we will find the magnitude and direction of given vector,

Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

A:

Q: Consider a 55-N weight suspended by two wires as shown in the accompanying figure. If the magnitude…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (a) Calculate the dot product and angle between two vectors, where u 7j– 2k and v = (1,2,3).

A:

Q: Find the value of a in the vector i = (a, b) if b = 48 and ||ū|| = 50 %3D v is in Quadrant I

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Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

A:

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: The volume of the parallelepiped determined by the vectors a =,b= and c = is: %3D (A) 12 (B) 6 (C)…

A: This question is related to volume of parallelepiped, we will solve it by using the formula of…

Q: Assuming vector B is 12 units long, vector 4B is:

A:

Q: The volume of the parallelepiped determined by the vectors ä =,b = and č = is: (A) 12 (B) 6 (C) 24…

A:

Q: Find the unit vector that has the same direction as the given vector. −3i + 7j

A: Given data: The given vector is a=-3i+7j. The modulus of the given vector is, a=-32+72=9+49=58 The…

Q: Q:: Find the area of parallelogram whose sides are a = 2i – 4j + 5k and b = i – 2j – 3k. Also find…

A:

Q: (d) Explain why each vector VER can be expressed in precisely one way as v u+w, where u ES and w ES.

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.