Question

# The line x+65=y+103=z+148 is the hypotenuse of an isosceles right-angled triangle whose opposite vertex is (7,2,4). Then which of the following is not the side of the triangle?

A
x72=y23=z46
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x73=y26=z42
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x73=y25=z41
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C x−73=y−25=z−4−1Let opposite vertex be A(7,2,4). x+65=y+103=z+148=λ Hence, any point on above line be B≡(5λ−6,3λ−10,8λ−14) Direction ratios of line AB are (5λ−13,3λ−12,8λ−18) Direction ratios of line BC are (5,3,8). Since, the angle between AB and BC is π/4. ∴cosπ4=(5λ−3)5+3(3λ−12)+8(8λ−18)√52+32+82.√(5λ−13)2+(3λ−12)2+(8λ−18)2 Squaring and solving, we get λ=3,2 Hence, equation of lines are x−72=y−2−3=z−46 and x−73=y−26=z−42

Suggest Corrections
0
Related Videos
Angle between Two Line Segments
MATHEMATICS
Watch in App