Check whether the vector `4hat i+ 13hat j-18hat k` is a linear combination of the vectors `hat i-2hat j+3hat k and 2hat i+3hat j-4hat K`.

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is

The unit vector which is orthogonal to the vector 5hat j+2hat j+6hat k and is coplanar with vectors 2hat i+hat j+hat k and hat i-hat j+hat k is (2hat i-6hat j+hat k)/(sqrt(41)) b.(2hat i-3hat jmath)/(sqrt(13)) c.(3hat i-hat k)/(sqrt(10))d.(4hat i+3hat jmath-3hat k)/(sqrt(34))

Express the vector bar(a)=9hat(i)+hat(j)+2hat(k) as a linear combination of the vectors bar(q)=-hat(i)-hat(j)+2hat(k)andbar(r)=3hat(i)+hat(j)-hat(k) .

The magnitude of the vector product of the vector hat i+hat j+hat k with a unit vector along the sum of vectors 2hat i+4hat j-5hat k and lambda i+2hat j+3hat k is equal to sqrt(2). Find the value of lambda_(.)