Condition for Two Lines to Be Perpendicular
Trending Questions
Q. Let two lines L1:x−33=y−2−4=z−1 and L2:x−34=y−21=z−3 and x−3a=y−26=zb, (a, b∈R) is the acute angle bisector between lines L1 and L2. Then the value of |a+b|=
Q. If l1, m1, n1 and l2, m2, n2 are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be
- (m1n2−m2n1), (n1l2−l1n2), (l1m2−l2m1)
- (l1l2−m2m1), (m1m2−n1n2), (n1n2−l2l1)
- 1√l21+m21+n21, 1√l22+m22+n22, 1√3
- 1√3, 1√3, 1√3
Q. If the co-ordinates of the points P and Q be (1, -2, 1) and (2, 3, 4) and O be the origin, then
- OP ⊥ OQ
- OP = OQ
- None of these
- OP || OQ
Q.
A line l passing through the origin is perpendicular to the lines
l1:(3+t)^i+(−1+2t)^j+(4+2t)^k, −∞<t<∞l2:(3+2s)^i+(3+2s)^j+(2+s)^k, −∞<s<∞
Then, the coordinate(s) of the point(s) on l2 at a distance of √17 from the point of intersection of l and l1 is (are)
(73, 73, 53)
−1, −1, 0
(1, 1, 1)
(79, 79, 89)
Q.
From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = -x, z = -1. If P is such that ∠QPR is a right angle, then the possible value(s) of
λ is (are)
1
-1
√2
−√2
Q. Column I Column IIa. Lines x−1−2=y+23=z−1 and →r=(3^i−^j+^k)+t(^i+^j+^k) are p. intersectingb. Lines x+51=y−37=z+33 and x−y+2z−4=0=2x+y−3z+5=0 are q. perpendicularc. Lines (x=t−3, y=−2t+1, z=−3t−2) and →r=(t+1)^i+(2t+3)^j+(−t−9)^k are r. paralleld. Lines →r=(^i+3^j−^k)+t(2^i−^j−^k) and →r=(−^i−2^j+5^k)+s(^i−2^j+34^k) are s. skew
Then which of the following is correct ?
Then which of the following is correct ?
- a→q, s; b→r; c→p, q; d→p
- a→q; b→r; c→p, q; d→p, q
- a→s; b→r, s; c→p; d→p, q
- a→q, s; b→r, s; c→p; d→p
Q. Equation of a line in the plane π:2x−y+z−4=0 which is perpendicular to the line l whose equation is x−21=y−2−1=z−3−2 and which passes through the point of intersection of l and π is
- x−21=y−15=z−1−1
- x+22=y+1−1=z+11
- x−22=y−1−1=z−11
- x−13=y−35=z−5−1
Q. If the two lines x+(a−1)y=1 and 2x+a2y=1, (a∈R−{0, 1}) are perpendicular, then the distance of their point of intersection from the origin is :
- √25
- 2√5
- √25
- 25
Q. If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (α, 7, 1) is (53, 73, 173), then α is equal to
Q. If the lines x=ay+b, z=cy+d and x=a′z+b′, y=c′z+d′ are perpendicular, then :
- ab′+bc′+1=0
- bb′+cc′+1=0
- aa′+c+c′=0
- cc′+a+a′=0