The point $A\,$ has position vector

$a=5i−3j+4k\mathbf{a} = 5\mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$ .

The point $P\,$ has position vector $p=λi+2j+k\mathbf{p} = \lambda\mathbf{i} + 2\mathbf{j} + \mathbf{k}$ , where $\lambda\,$ is a constant.

Show that $∣AP⃗∣2=λ2−10λ+59\left|\vec{AP}\right|^2 = \lambda^2 - 10\lambda + 59$ .

Find the value of $\lambda\,$ for which $∣AP⃗∣\left|\vec{AP}\right|$ is least, and state that least value in exact form.

Find the set of values of $\lambda\,$ for which $∣AP⃗∣>7\left|\vec{AP}\right| > 7$ .

The point $A\,$ has position vector

$a=5i−3j+4k\mathbf{a} = 5\mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$ .

The point $P\,$ has position vector $p=λi+2j+k\mathbf{p} = \lambda\mathbf{i} + 2\mathbf{j} + \mathbf{k}$ , where $\lambda\,$ is a constant.

Show that $∣AP⃗∣2=λ2−10λ+59\left|\vec{AP}\right|^2 = \lambda^2 - 10\lambda + 59$ .

Find the value of $\lambda\,$ for which $∣AP⃗∣\left|\vec{AP}\right|$ is least, and state that least value in exact form.

Find the set of values of $\lambda\,$ for which $∣AP⃗∣>7\left|\vec{AP}\right| > 7$ .

1.11 Vectors

1.11 Vectors Questions