2. The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane. (a) Find the vectors PQ, PŘ and PT. Then find a pair of linearly independent vectors among PQ, PŔ and PT. (b) Find the angle 0 between the two linearly independent vectors found in part (a). (c) Use your answers in part (a) to find an equation of the plane containing the points P Q, R and T in the standard form.

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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,

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Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

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A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

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Q: Given two vectors P=a,-a, Q-2а, -а, ta, R=2a,+3a,+a, Determine: (a). (P+Q)x(P-Q) (b). Q.RxP (c)…

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

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Q: 18. Find the projection of (0,4) onto (3,7).

A: Answer

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

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Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

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Q: Find the values of x such that the angle between the vectors and is 45°.

A: Given that The angle between the vectors 6,1,-1 and 1,x,0 is 45°.

Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

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Q: mine the angle between vectors M = (1

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Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

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Q: Find the projection of v = [-3, 3, 6] onto the line L with vector equation x=td where d = [4, -3, 1]

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