[" What product of a vector with vertices "3vec c" -svec k "],[" 2,"177" ? and "7" it "2" the are "1,6" and "],[" respectively.Find the veotor "]

Dot products of a vector with vectors 3hat i-5hat k,2hat i+7hat j and vec a=hat i+hat j+hat k are respectively -1,6 and 5. Find the vector.

Dot products of a vector with vectors 3 hat i-5 hat k ,2 hat i+7 hat ja n d vec a= hat i+ hat j+ hat k are respectively -1, 6 and 5. Find the vector.

Dot product of a vector with vector 3hat(i)-5hat(k),2hat(i)+7hat(j)andhat(i)+hat(j)+hat(k) are respectively -1,6 and 5. Find the vector.

5. Dot product of a vector with vectors 37-5k, 27+7j and i +j+k are respectively -1,6and 5. The vector is 1) 37 +j+2k 2) 37 +2k 3) 37-2k

Find the unit vector in the direction of vector vec PQ ,P(1,2,3) and Q(5,6,7 )

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.

vec [AB]=3hat i+ hat j+ hat k and vec [CD]= -3hat i+2 hat j+4 hat k are two vectors. The position vectors of points A and C are 6 hat i+ 7 hat j+ 4 hat k and -9 hat j +2 hat k respectively. Find the position vector of point P on the line AB and point Q on the line CD such that vec [PQ] is perpendicular to vec [AB] and vec [CD] both.

Define the vector product of two vectors vec a and vec b . If vec a = 2 hat i- hat j+ hat k and vec c= 2 hat i+ 3 hat j , then find (vec a+ vec b)* vec c and vec a* (vec b+ vec c) .