The moment about a line through the origin having the direction of 1 12hati -4hatj -3hatk` is

A force of 39 kg. wt is acting at a point p ( -4,2,5) in the direaction 12hati -4hatj -3hatk . The moment of this force about a line through the origin having the direction of 2hati -2hatj + hatk is

Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the direction perpendicular to the direction of vector veca = hati + hatj +hatk is hati - hatj Statement 2: A component of vector in the direction of veca = hati + hatj + hatk is 2hati + 2hatj + 2hatk

Find the equation of a line passes through the points whose position vectors are (hati+4hatj+hatk) and (2hati-hatj+5hatk) .

The position vector of the point in which the line joining the points hati-2hatj+hatk and 3hatk-2hatj cuts the plane through the origin and the points 4hatj and 2hati+hatk is

The equation of plane which passes through the point of intersection of lines vecr=hati+2hatj+3hatk+lamda(3hati+hatj+2hatk) and vecr=3hati+hatj+2hatk+mu(hati+2hatj+3hatk) where lamda,muinR and has the greastest distance from the origin is :

A line passes through the point with position vector 2hati-hatj+3hatk and is in the direction of hati+hatj-2hatk . Find the equation of the line in vector and Cartesian forms.

Find the equation of the plane through the intersection of the planes. vecr. (hati+3hatj-hatk)=9 and vecr. (2hati-hatj+hatk)=3 and passing through the origin.

The direction cosines of the vector 3hati-4hatj+5hatk are

The direction cosines of the vector 3hati-4hatj+5hatk are

The perpendicular distance from the origin to the plane through the point (2,3,-1) and perpendicular to the vector 3hati-4hatj+7hatk is