Hi Harsh.

I've re-written your question using bold face for the vector quantities and regular face for the scalar quantities:

Two vectors U= U_x i -6j +k And V= -3i +V_y j +k. Their dot product U•V= -35. AND the magnitude of their sum is |U+V|= 3. What are the components of U_x and V_y ?

The dot product of two three-dimensional vectors is computed by adding together the products of the components in the same direction. In your question, this means

-35 = U•V = -3U_x - 6V_y + 1

The sum of these two vectors is simply the vector whose components are the sums of the components in the same direction:

U + V = (U_x - 3)i + (V_y - 6)j + 2k

And the magnitude of any vector is the square root of the sum of the squares of its components, so the magnitude of U + V is:

3 = |U + V| = sqrt( (U_x - 3)² + (V_y - 6)² + 2² )

Now you have two equations with two unknowns. Can you finish the question now?

Hope this helps,
Stephen La Rocque.