To find the vector equation of the line passing through the point (1, 2, 3) and parallel to the given planes, we can follow these steps:Step 1: Identify the Position Vector The position vector of the point (1, 2, 3) can be repr
To find the vector equation of the line passing through the point (1,2,3) and parallel to the given planes, we can follow these steps: Step 1: Identify the normal vectors of the planesThe equations of the planes are given in the dot product form: 1. →r⋅(^i−^j+2^k)=02....
Since, the line is perpendicular to plane, therefore it is parallel to it's normal vector.If a point on a line a and a vector parallel to it q is known, then the equation of line is r=a+λ q.Hence, the equation of the required line, passing through point 2 i+ j+4 k and ...
The Line Integral of the Vector Field: The line integral of the vector field is about evaluating the integral of the vector field along the given curve. The following notation is the formula evaluating this line integral ...
【解析】In Section we found a vector equation for theline segment that joins the tip of the vector roto the tip of the vector r:r(t)=(1-t)ro+t 10≤t≤1Here we take r_0=(1,3,-2) and r_1=(2,-1,3) to obtain a vector equation of the line segment fromp to q:r(t)=(...
Answer to: Find the vector equation for the line of intersection of the planes x+4y-4z=-5 \enspace and \enspace x+5z=-2 By signing up, you'll get...
The equation of a line is linear in two variables, usually x and y, that is satisfied by points of the line. The equation of line is usually found by the point-slope form y - y_1 = m (x - x_1), where m is the slope and (x_1, y_1) is a point on the line.
Find the vector equation of the plane passing through (2,3,5) and having a normal vector 3i-j-k. Find the unit normal vector N(t) to r(t) = (7, sin 10t, cos 10t). Find a normal vector for the plane in R^3 which contains the lines (x, y, z) = (1...
The line through the point(1,0,2)and perpendicular to the planex+4y+z=5 r(t)= Need Help? There are 2 steps to solve this one. Step 1 Solution We have to find the equation of line passes through the given point (1,0,2) and perpen...
(1)(0,2,6), (1,3,2) and (-1,2,4) (2)(3,1,2), (0,4,0) and (0,0,1) (3)(2,0,3), (0,-1,2) and (4,-3,0). 相关知识点: 试题来源: 解析 (1)ⅱ -2x+6y+z=18 (2)ⅱ -5x+3y+12z=12 (3)ⅱ -y+z=3 {many vector forms exist} 反馈 收藏 ...