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Find the unit vector perpendicular to each of the vectors 6i + 2j + 3k and 3i – 2k.

A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known... View Article

The formula to find the slant height of the cone is

The slant height of the cone of height h and radius r is given by l = √h2 + r2.... View Article

Can two obtuse angles be supplementary?

No, two obtuse angles cannot be supplementary angles.... View Article

The diagonal AC of a parallelogram ABCD bisects angle A. Show that it bisects angle C also.

Given a parallelogram ABCD. ∠1 = ∠2 ---- (1) To show that AC bisects ∠C that is ∠3 = ∠4. Proof: ∠1 = ∠2 (given) ∠2 = ∠3 [alternate angles... View Article

Given that kx (x – 2) + 6 = 0 has real and equal roots, the root is

The given expression is... View Article

Without actually calculating the cubes, find the value of the following: ((- 12)³ + (7)³ + (5)³).

The given expression is... View Article

The smallest rational number is

The smallest rational number doesn’t exist.... View Article

The value of tan 30 tan 60 is

tan 30 tan 60 = (1 / √3) √3 = 1... View Article

If sec α and cosec α are the roots of the equation x² – px + q = 0, then prove that p² = q (q + 2).

The given equation is x2 - px + q = 0 sec α and cosec α are the roots of the equation.... View Article

The harmonic mean of the roots of the equation (5 + √2) x² – (4 + √5) x + 8 + 2 √5 = 0 is

Let be the roots of given quadratic equation.... View Article

Simplify a (a² + a + 1) + 5 and find its value for a = 1.

Consider... View Article

Find the multiplicative inverse of (2 – √3) / (2 + √3).

To find the multiplicative inverse of the given expression.... View Article

Solve 4z + 3 = 6 + 2z for the value of z.

4z + 3 = 6 + 2z 4z - 2z = 6 - 3 2z = 3 z = 3 / 2... View Article

Two supplementary angles differ by 48 degrees. Find the angles.

The two supplementary angles are differed by 48 degrees. Let the angle measured is x degrees. Its supplementary angle will be (180 - x)... View Article

If 2x + 3 = x – 4 then the value of x is

2x + 3 = x - 4 ⇒ 2x - x = - 4 - 3 ⇒ x = - 7... View Article

If ⁿC₈ = ⁿC₂ find ⁿC₂.

The given expression is of the form of... View Article

How many lines of symmetry does an octagon have?

A regular octagon has 8 lines of symmetry.... View Article

Explain the scalar product of two vectors.

The dot product/scalar product of two vectors is the product of the magnitude of 1 vector and the magnitude of the component of another vector in... View Article

The standard form of 192 / – 168 is

192 / - 168 = - 192 / 168 = - [2 * 3 * 4 * 8] / [2 * 3 * 4 * 7] = - 8 / 7... View Article

If all the sides of a parallelogram touch a circle, then the parallelogram is

If all the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.... View Article

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