Question

Question 71
Let O be the origin and P(-2, 4) be a point in the xy plane. Express OP in terms of vectors
and j also find OP
415
55
315
225
Clear Answer​

Answer 1

Step-by-step explanation:

The coordinates of the origin are $\mathsf{O(0,0)}$ which in terms of vectors be $\mathsf{(0\hat{i}+0\hat{j})}$.

The coordinates of the given point are $\mathsf{P(-2,4)}$ which in terms of vectors be $\mathsf{(-2\hat{i}+4\hat{j})}$.

Thus the vector $\mathsf{\vec{OP}}$

$\mathsf{= position\:vector\:of\:P - position\:vector\:of\:O}$

$\mathsf{=(-2\hat{i}+4\hat{j})-(0\hat{i}+0\hat{j})}$

$\mathsf{=-2\hat{i}+4\hat{j}}$

Also, $\mathsf{OP=|\vec{OP}|=\sqrt{(-2)^{2}+4^{2}}}$ units

$\Rightarrow \mathsf{OP=\sqrt{4+16}}$ units

$\Rightarrow \mathsf{OP=\sqrt{20}}$ units

$\Rightarrow \mathsf{OP=2\sqrt{5}}$ units

Answer:

$\mathsf{\vec{OP}=-2\hat{i}+4\hat{j}}$

$\mathsf{OP=2\sqrt{5}}$ units