The sum of all possible real values of '...

The sum of all possible real values of ' a ' for which vectors ` vecr_1= ln |a| hati+a hatj-hatk` and `vecr_2=(1+a^2) hati-hatj` `(a-1) hatk` are orthogonal is

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Find the value of lambda for which the vectors veca = 3hati + 2hatj + 9 hatk and vecb = hati + lambda hatj + 3hatk are orthogonal.

Find the distance between the planes vecr*(hati-2hatj-2hatk)=7 and vecr*(5hati-10hatj-10hatk)=15.

Show that the vectors veca=2hati+3hatj+6hatk,vecb=6hati+2hatj-3hatk, " ""and"" "vecc=3hati-6hatj+2hatk , are mutually orthogonal.

Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5hatkandvecc=hati-6hatj--7hatk .

Find the acute angle between the planes vecr(2hati-3hatj+5hatk)=1 and vecr(hati-hatj-hatk)=7 .

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to x axis.

The value of [hati - hatj , hatj - hatk, hatk - hati] is :

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is

Find the equation of the plane passing through the line of intersection of the plane vecr*(2hati+3hatj-4hatk)+1=0 and vecr*(hati-hatj+3hatk) =3 and through the point (1, 1, -1).

The co-ordinates of the point P on the line vecr =(hati +hatj + hatk)+lambda (-hati +hatj -hatk) which is nearest to the origin is

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