nd the length of the vector fo raight line joining the points 5,2). Also find the angle made

Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR 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 lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: The vector with length 4 and direction k is Di+Di+ j+ k.

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Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: Let a = (2, – 3) and b (0, – 3). - - Find the angle between the vector, in degrees.

A: Given a→=<2,-3>           b→=<0,-3>

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

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Q: find the acute angle between the given linesby using vectors parallel to the lines. y = x, y = 2x +…

A: Here the acute angle between two lines is to be calculated.

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: Let 0 be the angle between vectors A and B, find the value of the angle 0 when -6V3A × B = 18Ã. Ē

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Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Suppose that |u| = 10 and |v| = 7, and that u • v = -55. Find the angle θ between the vectors u and…

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (2, 5, 3), Q = (– 3, –…

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Q: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: a/The angle between the two vectors A2 Bz 3 TT 2

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: Find the angle between vectors: a = 51-4j+2k and, b= 41+3)+2√5k

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Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

A: Given points are P(2, 7) and Q(6, 4).

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

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

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Q: Let L be the line 8x + 2 in R?. Find vectors a and b so that v a + tb with t ER is also a correct…

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Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

A: .

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: The inner(dot) product of two vectors and with lengths a and b. is given by a-b = abcos(y+2 T) ,…

A: The statement is true. The given statement is true because , Given a→.b→=abcosγ+2π But, cos…

Q: The angle between the two vectors u = (4, 7) and v = (11 /2, 3 /2) computed via the cosine formula…

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Q: Find the area of the parallelogram with vectors a = 3p+ 2q, b= 2p-qwhere \pl = 4, lq] = 3, (p, q)…

A: To find the area of the parallelogram with the vectors a=3p+2q,b=2p-q where p=4,q=3,p,q=3π4.

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

Q: Find the vector v that has magnitude 3| and makes the angle 0 = n with the positive x-axis. v = help…

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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: Let u =⟨2,2,1⟩which makes an angle of 30∘ with v. If the dot product of vector u and v is 6. What is…

A: Given:   To determine: The magnitude of vector v

Q: Find the angle θ between the two vectors.u = (10, −5, 15), v = (−2, 1, −3)

A: The given vectors are To find the angle between the given vectors, use the formula

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

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Q: For what value of "c" are the following vectors perpendicular? 3 (2, с, 9) аnd ў 3 (Зс, —1,5) (Зс, —…

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Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

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Q: Suppose that |u| = 6 and |v| = 9, and that u times v = -37. Find the angle θ between the vectors u…

A: Vector Question

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…