Answer: When you know the normal vector of a plane and a point passing through the plane, the equation of the plane is established as **a (x – x1) + b (y– y1) + c (z –z1) = 0**.

**There is no difference between saying two lines are perpendicular** and that one line is normal to another line. It is literally a synonymous term, like saying that you take the product of two numbers or you multiply two numbers.

Normal Form

Then the equation of the line will be **x cos ω + y sin ω = p** , where p is the length of perpendicular & ω is the angle perpendicular makes with positive x axis.

Answer: When you know the normal vector of a plane and a point passing through the plane, the equation of the plane is established as **a (x – x1) + b (y– y1) + c (z –z1) = 0**.

**The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right by invertible square matrices**. In particular, the integers are a PID, so one can always calculate the Smith normal form of an integer matrix.

The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, **a canonical form specifies a unique representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness**.

In summary, normal vector of a curve is the derivative of tangent vector of a curve. To find the unit normal vector, we simply divide the normal vector by its magnitude: **ˆN=dˆT/ds|dˆT/ds|ordˆT/dt|dˆT/dt|**.

Following are the various types of Normal forms:

Normal Form | Description |
---|---|

BCNF | A stronger definition of 3NF is known as Boyce Codd's normal form. |

4NF | A relation will be in 4NF if it is in Boyce Codd's normal form and has no multi-valued dependency. |

The normal vector, often simply called the "normal," to a surface is **a vector which is perpendicular to the surface at a given point**. When normals are considered on closed surfaces, the inward-pointing normal (pointing towards the interior of the surface) and outward-pointing normal are usually distinguished.

One way to find a vector perpendicular to a given vector in 3 dimensions is to **take the cross-product with another (non-collinear) vector**. For example, (1,0,0)×(1,2,3)=(0,−3,2) is perpendicular to both (1,0,0) and (1,2,3), as you can verify by showing their dot product is 0.

The normal is **a line at right angles to the tangent**. If we have a curve such as that shown in Figure 2, we can choose a point and draw in the tangent to the curve at that point. The normal is then at right angles to the curve so it is also at right angles (perpendicular) to the tangent.

**Boyce-Codd Normal Form** is an advanced version of the third normal form in database normalization. It is the strictest, highest and most efficient form of Normalization since it eliminates the condition that allowed the right side of the functional dependency to be a prime attribute in 3NF.

Equation of Straight Line

The relation between variables x, y satisfy all points on the curve. The general equation of straight line is as given below: **ax + by + c = 0** { equation of straight line.

There will be 1/4^{th} negative marking for each wrong answer. Those who qualify through the IBPS PO objective round will qualify for the IBPS mains written examination (**descriptive in nature)**.

**Six step guide to help you solve problems**

- Step 1: Identify and define the problem. State the problem as clearly as possible.
- Step 2: Generate possible solutions.
- Step 3: Evaluate alternatives.
- Step 4: Decide on a solution.
- Step 5: Implement the solution.
- Step 6: Evaluate the outcome.

It is supported by various donors who enable the platform to produce content at scale for its millions of students worldwide. **Khan Academy earns money as a charitable organization** through grants, tuition fees out of its Khan Lab School, and payments for its SAT prep courses.

The Prelims and Mains both are completely objective tests, and **there are no descriptive type questions** in the IBPS Clerk exam. The total time allotted for the exam is 1 hour.

**How To Do Long Multiplication**

- Arrange the numbers one on top of the other and line up the place values in columns.
- Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.
- Write the answer below the equals line.

**So, on the basis of size, there are five types of computers:**

- Supercomputer.
- Mainframe computer.
- Minicomputer.
- Workstation.
- PC (Personal Computer)

Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient. Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it.

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22-Jul-2022

Education