If I was given two-equation of two planes. To find a vector parallel to the plane, do I take the cross product of two normal vectors of the two given planes?

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

A: I am attaching image so that you understand each and every step.

Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: Define the term Parallel Vectors?

A: Parallel vectors: The vectors that are parallel if they have the same direction.

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: A normal vector for the plane through the points (2, 5, 1),(3, 7, 0), and (2, 5, 2) is _____ .

A: Given ,            (2,5,1) , (3,7,0), and (2,5,2)

Q: What is meant by the term translation in vectors?

A:

Q: How is the angle between two vectors defined and how is it computed?

A: the angle between two vectors is computed using cosθ

Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

Q: Find an equation of the plane that passes through the point P(-8, –3, 7) and has the vector n = (-8,…

A:

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: would two independent vectors span a plane whereas two dependent vectors span a line?

A: If two vectors are linearly dependent:

Q: What is the dot product of a vector with the cross product that this vector has with another vector?

A:

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

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: Find the vector with length V17 and same direction as = (7,0, -6).

A:

Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

Q: Given a position vector v, why are there infinitely many vectors equal to v?

A: For given position vector, there are infinitely many translations possible. It is known that the…

Q: Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose…

A: We will first find direction of vector using the magnitude and values of initial point and parallel…

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: We say that two vectors are equivalent .if they have the same components

A: Ginen statement, Two vectors are equivalent if  they have same component.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

Q: Find the dot product of vectors and .

A:

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: What is the magnitude of the cross product of two parallel vectors?

A:

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

Q: Find an equation of the plane that passes through the point P(-5, –8,8) and has the vector n = (-8,…

A:

Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

A: Given problem:- Find an equation of the plane that passes through the point P(-8, -4,7) and has the…

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: A normal vector for the plane through the points (2, 5, 1), (3, 7, 0), and (2, 5, 2) is <

A:

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

A:

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A:

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: 8

A: Given vector is v→=8-7-5 We have been asked to find two linearly independent vectors that are…

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

Q: Consider the vectors ā (2, 3, –1) and b = (4, –9, 6). Find the cross product of a and b

A:

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

A:

Q: How do we know if two nonzero vectors are perpendicular?

A: Two non-zero vectors are perpendicular if their dot product is zero.

Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

Q: If we were to decompose the vector , what would be the vertical component?

A:

Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

A:

Q: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

A: The dot product of two vectors is also equal to the product of their __________ multi-plied by the…

Q: What are parallel vectors?

A: We have to define parallel vectors. Two vectors are said to be parallel if they have same direction…

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…