If `vecr.(2hati+3hatj-2hatk)+3/2=0` is the equation of a plane and `hati-2hatj+3hatk` is a point then a point equidistasnt from the plane on the opposite side is
(A) `hati+2hatj+3hatk` (B) `3hati+hatj+hatk` (C) `3hati+2hatj+3hatk` (D) `3(hati+hatj+hatk)`

Find the angle between the following pairs of vectors 3hati+2hatj-6hatk, 4hati-3hatj+hatk , hati-2hatj+3hatk, 3hati-2hatj+hatk

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

Let veca=hatj-hatk and vecc=hati-hatj-hatk . Then the vector vecb satisfying vecaxxvecb+vecc=0 and veca.vecb=3 is (A) -hati+hatj-2hatk (B) 2hati-hatj+2hatk (C) hati-hatj-hatk (D) hati+hatj-2hatk

Let veca=hati+2hatj +hatk, vec=hati-hatj+hatk and vecc=hati+hatj-hatk . A vector in the plane of veca and vecb whose projection on vecc is 1/sqrt(3) is (A) 4hati-hatj+4hatk (B) hati+hatj-3hatk (C) 2hati+hatj-2hatk (D) 4hati+hatj-4hatk

The vector (s) equally inclined to the vectors hati-hatj+hatk and hati+hatj-hatk in the plane containing them is (are_ (A) (hati+hatj+hatk)/sqrt(3) (B) hati (C) hati+hatk (D) hati-hatk

The vector equation of the plane passing through the points hati+hatj-2hatk,2hati-hatj+hatk and hati+hatj+hatk , is

Find the equation of the plane through the point (3,4,-5) and parallel to the vectors 3hati+hatj-hatk and hati-2hatj+hatk .

Vectors perpendicular to hati-hatj-hatk and in the plane of hati+hatj+hatk and -hati+hatj+hatk are (A) hati+hatk (B) 2hati+hatj+hatk (C) 3hati+2hatj+hatk (D) -4hati-2hatj-2hatk

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr= 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk) .

Let veca=2hati+hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hatk be three vectors . A vector in the plane of vecb and vecc whose projection on veca is of magnitude sqrt((2/3)) is (A) 2hati+3hatj+3hatk (B) 2hati+3hatj-3hatk (C) -2hati-hatj+5hatk (D) 2hati+hatj+5hatk