Image of the point P with position vector `7hat i- hat j+ 2hat k` in the line whose vector equation is , `vec r =9hat i + 5 hat j+ 5hat k + lambda(hat i+ 3hat j+ 5hat k)` has the position vector

Image of the point P with position vector 7hat(i) - hat(j) + 2hat(k) in the line whose vector equation is vec(r) = 9hat(i) + 5hat(j) + 5hat(k) + lambda(hat(i) + 3hat(j) + 5hat(k)) has the position .

Show that the plane whose vector equation is vec r*(hat i+2hat j=hat k)=3 contains the line whose vector equation is vec r*(hat i+hat j)+lambda(2hat i+hat j+4hat k)

Show that the plane whose vector equation is vec r*( hat i+2 hat j= hat k)=3 contains the line whose vector equation is vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot

Find lambda if the vectors 5 hat i + 2 hat j - hat k and lambda hat i - hat j + 5 hat k are orthogonal.

If the four points with position vectors −2 hat i+ hat j+ hat k, hat i+ hat j + hat k, hat j – hat k and λ hat j+ hat k are coplanar, then λ=

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_(.)

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

Find the value of lambda for which the four points with position vectors - hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k and 4 hat i+4 hat j+4 hat k are coplanar.