IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and perpendicular to B is

Q: The unit vector which is perpendicular to both r1=8ax+3ay- 2az , r2=2ax+7ay-6az is equal to

A: Given, vectors arer1=8ax+3ay-2az, r2=2ax+7ay-6azThe unit vector perpendicular to both vectorsr1, r2…

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: Find the equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

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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: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non- %3D orthogonal because the dot…

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non-orthogonal because the dot…

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Q: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

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Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

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: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

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: 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 a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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Q: Consider the points A(1,−3,4), B(2,5,4) and C(1,1,6). Then the cross product AB × AC is the vector:…

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Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Find two linearly independent vectors perpendicular to the w 41 -6- 1

A: Given: vector is v→=4-91 we have to find the two linear independent vectors perpendicular the given…

Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors <1,-3,1> , <4,2,0> and passing through the point (3,0,-2)…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: Find the vector joining the points P1= (-3, 1) and P2= (5, 2) %3D %3D in terms of i and j.

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Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [2, -…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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Q: Find the cross products uxv and vxu for the the vectors u = 3i-j-2k and v=i+2j-3k.

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Q: value

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

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.