If vector `vec i+ 2vec j + 2vec k` is rotated through an angle of `90^@`, so as to cross the positivedirection of y-axis, then the vector in the new position is

The vector vec OA=-2hat i+hat j+2hat k tum by a right angle about origin (O) so that it passes through hat j+hat k, then vector in new position is

vec i + vec j + vec k, 4vec i + vec j + vec k, vec 4 + 5vec j + k Then the position vector of the circumcentre of the Delta ABC is

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.

Find lambda such that the scalar product of the vector vec i + vec j + vec k with the unit vector parallel to the sum of the vectors 2 vec i + 4 vec j - 5 vec k and lambda vec i + 2 vec j + 3 vec k is equal to 1.

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

For given vectors, vec a =2 hat i- hat j+2hat k and vec b =-hat i +hat j - hat k , find the unit vector in the direction of the vector vec a+ vec b .

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

If the vector vec a= x vec i + y vec j + 2 vec k is perpendicular to the vector vec b = vec i - vec j + vec k and the scalar product of vec a and vec c= vec i + 2 vec j is equal to 4 then x= ________ and y=__________.

If the vectors vec i-vec j,vec j+vec k and vec a from a triangle, then the possible vector vec a may be (A) -vec i-vec k (B) vec i-2vec j-vec k (C) 2vec i+vec j+vec k (D) vec i+vec k