`phati+3hatj+4hatk and sqrt(q)i+4hatk` are two vectors, where `p,q ge 0` are two scalars, the length of the vectors are equal then

Let p bari+3barj+4bark and sqrt(q)bari+5bark be two vectors where p, q ge 0 are two scalars. If (p, q) is a pair of values for which their lengths are equal, then there can be

vecA =2hati+3hatj+4hatk and vecB=hati-hatj+hatk are two vectors. Find vecAxxvecB .

Express the vector 2hati+3hatj+hatk as the sum of two vectors, one vector is perpendicualr to 2hati-4hatj+hatk and the other vector is parallel to 2hati-4hatj+hatk .

Let veca=2hati+phatj-3hatk and vecb=qhati-4hatj+2hatk be two vectors, if veca"||"vecb , then the values of p and q are -

If the vectors p hati + hatj+ hatk, hati i+ q hatj + hatk and hati + hatj + r hatk ( p ne q ne r ne 1) are coplanar, then the value of pqr- (p + q + r) is :

Forces 2hati+hatj, 2hati-3hatj+6hatk and -hati+2hatj-hatk act at a point P, with position vector 4hati-3hatj-hatk . Find the vector moment of the resultant of these forces about thepoint Q whose position vector is 6hati+hatj=3hatk