Show That the Lines (x+1)/3 = (y+3)/5 = (z+5)/7 and (x−2)/1 = (y−4)/3 = (z−6)/5 Intersect
Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7 and (x−2)/1=(y−4)/3=(z−6)/5 intersect, by finding parameter values that satisfy all three coordinate equations.
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Let a Straight Line L Pass Through P(2, −1, 3) and Be Perpendicular to the Lines (x−1)/2 = (y+1)/1 = (z−3)/(−2) and (x−3)/1 = (y−2)/3 = (z+2)/4. If L Intersects the yz-Plane at Q, Then the Distance Between P and Q Is
A line L through P(2,−1,3) is perpendicular to two given lines. Find where L meets the yz-plane and the distance PQ, using the cross product for L’s direction.
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If the Length of the Perpendicular From the Point (β, 0, β), β ≠ 0, to the Line x/1 = (y−1)/0 = (z+1)/(−1) Is √(3/2), Then β Is Equal To
The perpendicular distance from (β,0,β) to the line x/1=(y−1)/0=(z+1)/(−1) is √(3/2). Find β using the cross-product distance formula.
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Direction Cosines of the Line 5x−3=15y+7=3−10z
Find the direction cosines of 5x−3=15y+7=3−10z and a point through which it passes, by converting to symmetric form with equal-magnitude denominators.