A vector `10hat j` is rotated by `30^(@)` about its initial point in x- y plane in clockwise manner. The new vector is

A vector hati + sqrt(3) hatj rotates about its tail through an angle 60° in clockwise direction then the new vector is

A vector sqrt(3)hati + hatj rotates about its tail through an angle 30^(@) in clock wise direction then the new vector is

A vector 3i + 4j rotates about its tail through an angle 37° in anticlockwise direction then the new vector is

Position vector hat k is rotated about the origin by angle 135^0 in such a way that the plane made by it bisects the angle between hat i and hatj . Then its new position is

Position vector hat k is rotated about the origin by angle 135^0 in such a way that the plane made by it bisects the angel between hat ia n d hatjdot Then its new position is +-( hat i)/(sqrt(2))+-( hat j)/(sqrt(2)) b. +-( hat i)/2+-( hat j)/2-( hat k)/(sqrt(2)) c. ( hat i)/(sqrt(2))-( hat k)/(sqrt(2)) d. none of these

The plane x-y-z=4 is rotated through an angle 90^(@) about its line of intersection with the plane x+y+2z=4 . Then the equation of the plane in its new position is

A displacement vector of magnitude 4 makes an angle 30^(@) with the x-axis. Its rectangular components in x-y plane are

The vectors 2i+3 hat j ,5 hat i+6 hat j and 8 hat i+lambda hat j have initial points at (1, 1). Find the value of lambda so that the vectors terminate on one straight line.

The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a time form three planes, The three unit vectors drawn perpendicular to these planes form a parallelopiped of volume: ________________

Vectors vec a= hat i+2 hat j+3 hat k , vec b=2 hat i- hat j+ hat k and vec c=3 hat i+ hat j+4 hat k , are so placed that the end point of one vector is the starting point of the next vector. Then the vector are (A) not coplanar (B) coplanar but cannot form a triangle (C) coplanar and form a triangle (D) coplanar and can form a right angled triangle