Vector Algebra

Step 1: The vector representing the median through vertex is given by:
Step 2: Write the given vectors in component form:
Step 3: Add the vectors:
Step 4: Find the median vector:
Step 5: Length of the median:

Step 1: Distance of any point of line from plane:
Step 2: Multiply by direction scaling 5 → ≈10/3. Hence → (D).

Step 1: Identify the first term and common difference. Given A.P.: Step 2: Use the formula for the sum of first terms of an A.P. Given : Step 3: Simplify the expression. Step 4: Solve for . Step 5: Find the last term. The th term of an A.P. is: Step 6: Final conclusion. The last term of the A.P. is .

First, we find the cost of a single pen (unit cost).
Cost of 1 pen .
Cost of 1 pen .
Now, calculate the cost of 10 pens.
Cost of 10 pens .
Cost of 10 pens .