Q6 of 33 Page 11

Find the shortest distance between the following pairs of lines whose vector equations are :

and

Equation of line in vector form


Line I:




Line II:




Here,






The shortest distance between lines is












Putting these values in the expression,




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Find the vector and Cartesian equations of the line through the point (5, 2, –4) and which is parallel to the vector

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Find the angle between the following pairs of lines :

and

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Write the equation of the plane whose intercepts on the coordinate axes are 2, – 3 and 4.

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Find the vector and Cartesian equation of the plane which passes through the point (5, 2, -4) and perpendicular to the line with direction ratios 2, 3, -1.