Can you find at least one vector perpendiculr to `3hat(i)-4hat(j)+7hat(k)`?

Find the unit vector perpendicular to both 2hat(i) + 3hat(j)+ hat(k) and hat(i)-hat(j)+ 4hat(k)

What is the projection of the vector hat(i)-2 hat(j) + hat(k) on the vector 4hat(i) - 4hat(j)+ 7hat(k) ?

Show that four points whose position vectors are given 6hat(i)-7hat(j) ; 16hat(i)-19hat(i)-4hat(k) ; 3hat(i)-6hat(k) ; 2hat(i)-5hat(j)+10hat(k) are co-planar

Forces 2hat(i)+7hat(j),2hat(i)-5hat(j)+6hat(k),-hat(i)+2hat(j)-hat(k) act at a point P whose position vector is vec(4)-3hat(j)-2hat(k). Find the vector moment of the resultant of these forces acting at P about this Point Q whose position vector is 6hat(i)+hat(j)-3hat(k)

Show that the following vectors are coplanar : 3hat(i)-2hat(j)+4hat(k), 6hat(i)+3hat(j)+2hat(k), 5hat(i)+7hat(j)+3hat(k) and 2hat(i)+2hat(j)+5hat(k) .

What is the projection of the vector hat(i)-2hat(j)-hat(k) on the vector 4hat(i)-4hat(j)+7hat(k) ?