Coordinate Geometry MCQs with Answers

What is the unit vector of $\mathbf{A} = 8\mathbf{i} + 2\mathbf{j} + 2\mathbf{k}$?

• A.$\frac{1}{\sqrt{72}} (8\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$
• B.$\frac{1}{72} (8\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$
• C.$\frac{1}{\sqrt{68}} (8\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$
• D.$\frac{1}{8} (8\mathbf{i} + 2\mathbf{j} + 2\mathbf{k})$

A three-dimensional array of points, each of which has identical surroundings, is called?

• A.Bravais index
• B.Unit cell
• C.Crystal plane
• D.Space lattice

If $\sin\theta$ is positive and $\cos\theta$ is negative, in which quadrant does the angle $\theta$ lie?

• A.First quadrant
• B.Second quadrant
• C.Third quadrant
• D.Fourth quadrant

The vector which specifies only the direction of a given vector is called ?

• A.Zero vector
• B.Position vector
• C.Unit vector
• D.Co-initial vector

Past Paper MCQ

The point $(0, -7)$ lies in which quadrant?

• A.Quadrant II
• B.Quadrant III
• C.Quadrant IV
• D.Lies on Y-axis

If $\mathbf{A} = (a\mathbf{i} + b\mathbf{j})$ and $\mathbf{B} = 4(a\mathbf{i} + b\mathbf{j})$, then the magnitude of $\mathbf{A} \times \mathbf{B}$ is:

• A.$0$
• B.$4(a^2 + b^2)$
• C.$4\sqrt{a^2 + b^2}$
• D.$16(a^2 + b^2)$

The equation of a straight line with slope $m$ and $y$-intercept $c$ is?

• A.$y = c + mx^2$
• B.$x = my + c$
• C.$y = mx - c$
• D.$y = mx + c$

What is the cross product of vectors $(1, 0)$ and $(0, -1)$?

• A.$(0, 0, -1)$
• B.$0$
• C.$1$
• D.$-1$

The slope of the tangent to the curve $y^3x + y^2x^2 = 6$ at $(2, 1)$ is:

• A.$\frac{5}{14}$
• B.$-\frac{5}{14}$
• C.$\frac{14}{5}$
• D.$-\frac{14}{5}$

Magnitude of a vector can never be ?

• A.Zero
• B.Positive
• C.Negative
• D.Unity