Question:medium

The position vectors of the vertices $A$ and $B$ of a triangle $ABC$ are \[ \hat{i}+3\hat{j}+4\hat{k} \] and \[ 2\hat{i}+\hat{j}+2\hat{k} \] respectively. If \[ |AC|=5 \] and \[ \angle A=\frac{\pi}{3}, \] then \[ |BC|= \]

Show Hint

When coordinates of two vertices and an included angle are given, first find the known side using the distance formula and then use the cosine rule to determine the required side.

Updated On: Jul 29, 2026

$\sqrt{26}$
$3\sqrt{19}$
$3\sqrt{26}$
$\sqrt{19}$

Show Solution

The Correct Option is D

Solution and Explanation

Was this answer helpful?

Questions Asked in AP EAPCET exam

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

AP EAPCET - 2026
Differentiation

View Solution

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

AP EAPCET - 2026
Definite and indefinite integrals

View Solution

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

AP EAPCET - 2026
3D Geometry

View Solution

The position vectors of the vertices \(A\) and \(B\) of a triangle \(ABC\) are \[ \hat{i}+3\hat{j}+4\hat{k} \] and \[ 2\hat{i}+\hat{j}+2\hat{k} \] respectively. If \[ |AC|=5 \] and \[ \angle A=\frac{\pi}{3}, \] then \[ |BC|= \]

Show Hint

The Correct Option is D

Solution and Explanation

Top Questions on Product of Two Vectors

Questions Asked in AP EAPCET exam