The line of intersection of the planes `vecr.(3hati-hatj+hatk)=1` and `vecr.(hati+4hatj-2hatk)=2,` is (A) `(x-6/13)/2=(y-5/13)/-7=z/-13` (B) `(x-6/13)/2=(y-5/13)/7=z/-13` (C) `(x-4/7)/-2=y/7=(z-5/7)/13` (D) `(x-4/7)/-2=y/-7=(z+5/7)/13`

The line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2 is parallel to the vector (A) 2hati+7hatj+13hatk (B) -2hati+7hatj+13hatk (C) -2hati-7hatj+13hatk (D) 2hati-7hatj-13hatk

Find the distance of the point (3,4,5) from the plane vecr.(2hati-5hatj+3hatk)=13

The vector parallel to the line of intersection of the planes vecr.(3hati-hatj+hatk) = 1 and vecr.(hati+4hatj-2hatk)=2 is : a) -2hati-7hatj+13hatk b) 2hati+7hatj-13hatk c) 2hati+7hatj+13hatk d) -2hati+7hatj+13hatk

Find the angle between the following pairs of lines (i) veci=3hati+2hatj-4hatk+lambda(hati-2hatj+2hatk) and vecr=5hatj+hatk+mu(3hati+2hatj+6jhatk) (ii) vecr=hati+hatj+lambda(hati+2hatj+hatk) and vecr=mu(3hati+6hatj+4hatk) (iii) (x-1)/(2)=(y-2)/(3)-(z-1)/(-3) and (x+3)/(-1)=(y-5)/(8) = (z-1)/(4) (iv) (5-x)/(-2)=(y+3)/(-2)=(z-5)/(1) and (x+1)/(2) =(2y-3)/(4) = (z-2)/(1) (v) (x+3)/(1) = (y-1)/(2), z= 3 and (x-1)/(-2)=(y+3)/(3) = (z+5)/(4)

Show that the line vecr=(4hati-7hatk)+lambda(4hati-2hatj+3hatk) is parallel to the plane vecr.(5hati+4hatj-4hatk)=7 .

True or false The vector equation of the line (x-5)/3=(y+4)/7=(z-6)/2 is vecr=5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk) .

The length of the shortest distance between the two lines vecr=(-3hati+6hatj)+s(-4hati+3hatj+2hatk) and vecr=(-2hati+7hatk)=t(-4hati+hatj+hatk) is (A) 7units (B) 13units (C) 8units (D) 9units

Find the shortest distance between the following lines : (i) vecr=4hati-hatj+lambda(hati+2hatj-3hatk) and vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk) (ii) vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk) and vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk) (iii) (x-1)/(-1) = (y+2)/(1) = (z-3)/(-2) and (x-1)/(1) = (y+1)/(2) = (z+1)/(-2) (iv) (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/(3) = (y-3)/(4) = (z-5)/(5) (v) vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk) and vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)

Find the shortest distance between the following lines : (i) vecr=4hati-hatj+lambda(hati+2hatj-3hatk) and vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk) (ii) vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk) and vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk) (iii) (x-1)/(-1) = (y+2)/(1) = (z-3)/(-2) and (x-1)/(1) = (y+1)/(2) = (z+1)/(-2) (iv) (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/(3) = (y-3)/(4) = (z-5)/(5) (v) vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk) and vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)

The point of intersection of the pair of straight lines given by 6x^(2)+5xy-4y^(2)+7x+13y-2=0 , is