The two vectors j + k and 3 i - j + 4 k represent the two sides A… - Vidyadip

Question

The two vectors $\hat{\text{j}} + \hat{\text{k}}$ and $3\hat{\text{i}} - \hat{\text{j}} + 4\hat{\text{k}}$ represent the two sides AB and AC, respectively of a $\triangle \text{ABC},$ Find the length of the median through A.

✓

Answer

$\overrightarrow{\text{AD}} = \overrightarrow{\text{AB}} + \frac{1}{2}[\overrightarrow{\text{AC}} - \overrightarrow{\text{AB}}] = \frac{1}{2} (\overrightarrow{\text{AC}} + \overrightarrow{\text{AB}})$
$|\overrightarrow{\text{AD}}| =\frac{1}{2} |3\hat{\text{i}} + 5\hat{\text{k}}| = \frac{1}{2}\sqrt{34}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "1 Marks Question" from VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A coin is tossed three times, determine P(E|F),
where E: at least two heads, F: at most two heads.

Evaluate, $\int\limits_0^3\frac{\text{dx}}{9 + \text{x}^{2}}.$

A die is thrown three times. Events A and B are defined as below:
A: 4 on the third throw
B: 6 on the first and 5 on the second throw
Find the probability of A given that B has already occurred.

Integrate the functions in Exercises:
$\sqrt{\text{ax+b}}$

Find the rate of change of the area of a circle with respect to its radius r when r = 4 cm.

Write the value of $\sec^{-1}\Big(\frac{1}{2}\Big).$

g: {5, 6, 7, 8} → {1, 2, 3, 4} with
g = {(5, 4), (6, 3), (7, 4), (8, 2)}

Evaluate:
$\int (ax + b)^3 dx$.

Which of the given values of x and y make the pair of matrices equal
$\left[\begin{array}{cc} {3 x+7} & {5} \\ {y+1} & {2-3 x} \end{array}\right],\left[\begin{array}{cc} {0} & {y-2} \\ {8} & {4} \end{array}\right]$

Find $\int \frac{x^{4} d x}{(x-1)\left(x^{2}+1\right)}$