A line contains the points P=(−6,−2,−3)P=(-6,-2,-3) and Q=(−4,−3,−6)Q=(-4,-3,-6). A vector equation of this line is →x=−−→OP+t−−→PQx→=OP→+tPQ→, where OO is the origin. If t=2t=2, what point does this give us from the equation?

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: Write the equation of the line passing through P with normal vector n in normal form and general…

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Which of the following is a direction vector for the line through A (3, –2) and B(1, 2)? Select one:…

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Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

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Q: Which of the following Is a direction vector for the line through A(5, -3) and B(-1, 2)? Select one:…

A: For the direction vector, we just find out the direction of the given point.

Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: Let L₁ be the line passing through the points Q₁-(-1, -3, 1) and Q₂=(-4, -6, 2). Find a value of k…

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Q: Find the vector equation for the line of intersection of the planes 4x - y + 3z = 1 and 4x + 2z = −1…

A: Given:equation of two planes To find:vector equation of line that intersects these planes

Q: 1. A line passes through the points A(2, 3) and B(-2, 1). Determine a vector equation of the line.…

A: To determine the equation of line which passes through the points A(2,3) and B(-2,1).

Q: Find the vector equation for the line of intersection of the planes 5x + 3y2z = -1 and 5x + 5z = -4…

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