Find the vector a which is collinear with the vector `vec b = 2hat i-hat j and vec a.vec b=10`.

Let a vector vec(a) be coplanar with vectors vec(b) = 2hat(i) + hat(j) + hat(k) and vec(c) = hat(i) - hat(j) + hat(k) . If vec(a) is perpendicular to vec(d) = 3hat(i) + 2hat(j) + 6hat(k) , and |vec(a)| = sqrt(10) . Then a possible value of [[vec(a),vec(b),vec(c)]] + [[vec(a), vec(b), vec(d)]] + [[vec(a),vec(c),vec(d)]] is equal to :

What is the unit vector hat a parallel to the vector vec a= 3 vec I + 4 vec j - 2 vec k ? Find the vector vec b such that hat a + vec b becomes the unit vector vec i ?

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) .

Find the angle between the vectors vec a and vec b where: vec a=2hat i-3hat j+hat k and vec b=hat i+hat j-2hat k

Find the angle between the vectors vec a and vec b where: vec a=2hat i-hat j+2hat k and vec b=4hat i+4hat j-2hat k

If vec a=hat i+2 hat j+hat k and vec b=2 hat i+hat j and vec c=3 hat i-4 hat j-5 hat k , then find a unit vector perpendicular to both of the vectors vec a-vec b and vec c-vec b .

Find a unit vector in the direction of vec a- 2 vec b+ 3 vec c if vec a= hat i+ hat j , vec b= hat j+ hat k and vec c= vec i+ vec k .

Find the angle between the vectors vec a and vec b where: vec a=hat i-hat j and vec b=hat j+hat k

Find a unit vector perpendicular to each of the vector vec a+ vec b and vec a- vec b , where vec a=3 hat i+2 hat j+2 hat k and vec b= hat i+2 hat j-\ 2 hat k

Find a unit vector perpendicular to each of the vector vec a+ vec b and vec a- vec b , where vec a=3 hat i+2 hat j+2 hat k and vec b= hat i+2 hat j-\ 2 hat k