Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

Q: = Let -3 -1 -~--~--~--~--~- , V3 -5 1 , V₂ 2 0 combination of V₁, V2 and V3. 5 -26 , V4 -9 -1 -3…

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Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: A hiker realises that the sun is going down and she forgot her headlamp. If the surface of the…

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Q: Find (2x + 5y)dA where Ris the parallelogram with vertices (0,0), (-5,4), (-2,-1), and (-7,3). Use…

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Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Let ā = (1, 3,-1) and b (-1,0, 2). What is the y-component of ā x b %3D %3D 1 -1 3.

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Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

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Q: b Let a = (-3, 0, -1) and 6 = (3, -3, -2). Find the component of b onto a.

A: To find the component of vector b onto vector a, we use the formula: Component of b onto…

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

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Q: Find an expression for the exact angle 0 between u and v when = (4,7) and v = (-5, 8). (3, –1, 1)…

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Q: Show how v is orthogonal to any linear combination formed by w1 and w2

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Q: b Let a = (-3, 0, -1) and 6 = (3, -3, -2). Find the component of b onto a.

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: Find b and c so that y = 8x² + bx + c has vertex (7,5). b C =

A: Here given that y=8x2+bx+c and has the vertex at the point (7,5) since the line of symmetry is the…

Q: Express the following as a linear combination of u (2, 1, 5), v (1,-1, 4) and w = (6, 8, 6). (9, 14,…

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