If the vectors p⃗i + q⃗j and 3i - j perpendicular line g...

If the vectors \(\vec{p}i + \vec{q}j\) and \(3i - j\) perpendicular line \(g\) when \(p = 2\). (b). If the vectors \(m\) and \(n\) are such that \(|m| = 5\) and \(|n| = 12\) and the \(|m+n| = 13\). Find (i) The angle between \(m\) and \(n\). (ii) The scalar (dot product of \(m\) and \(n\))

Find the value of x if f(x) = 4x^3 - 26x^2 + 6x - 8. To find the value of x, we need to solve the equation f(x) = 0. 4x^3 - 26x^2 + 6x - 8 = 0 We can factor out a common factor of 2 from each term: 2(2x^3 - 13x^2 + 3x - 4) = 0 Now we can use synthetic division to find the roots of the equation. By trying different values of x, we find that x = 2 is a root of the equation. Using synthetic division, we divide 2x^3 - 13x^2 + 3x - 4 by (x - 2): 2 | 2 -13 3 -4 - 4 -18 -30 -------------- 2 -17 -15 -34 The result is 2x^2 - 17x - 15 - 34/(x - 2). Now we can factor the quadratic equation 2x^2 - 17x - 15 = 0: (2x + 3)(x - 5) = 0 Setting each factor equal to zero, we find two possible values for x: 2x + 3 = 0 --> x = -3/2 x - 5 = 0 --> x = 5 Therefore, the values of x that satisfy the equation f(x) = 0 are x = -3/2 and x = 5.

Adi S.

Question

If the vectors \(\vec{p}i + \vec{q}j\) and \(3i - j\) perpendicular line \(g\) when \(p = 2\). (b). If the vectors \(m\) and \(n\) are such that \(|m| = 5\) and \(|n| = 12\) and the \(|m+n| = 13\). Find (i) The angle between \(m\) and \(n\). (ii) The scalar (dot product of \(m\) and \(n\))

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