Question

PLZZ SOLVE THE QUESTION BELOW OF VECTORS CLASS 11:-

Answer 1

AnsWer :

(D) 5i + 8j.

Solution :

Taking Vector-1.

We have Two Compounds, Let A and B.

• Angle be 45°.
• Compound (A) 6√2 Cos 45°.
• Compound (B) 6√2 Sin 45°.

Compound A.

$\tt \dashrightarrow 6 \sqrt{2} \cos45 \degree.$

$\tt \dashrightarrow 6 \sqrt{2} \times \frac{1}{ \sqrt{2} } .$

$\tt \dashrightarrow - 6 \hat{i}$

Negative sign, because this vector show opposite sides of x- axis.

Compound B.

$\tt \dashrightarrow 6 \sqrt{2} \sin45 \degree.$

$\tt \dashrightarrow 6 \sqrt{2} \times \frac{1}{ \sqrt{2} } .$

$\tt\dashrightarrow 6 \hat{j}.$

It show upward direction with y- axis.

$\rule{200}1$

Taking Vector-2.

We have Two Compounds, Let A and B.

• Angle be 37°.
• Compound (A) be 10 Cos 37°.
• Compound (B) be 10 Sin 37°.

Compound A.

$\tt\dashrightarrow 10 \cos37 \degree.$

$\tt\dashrightarrow 10 \times \frac{4}{5} .$

$\tt\dashrightarrow 8 \hat{i}.$

Compound B.

$\tt\dashrightarrow 10 \sin37 \degree.$

$\tt\dashrightarrow 10 \times \frac{3}{5} .$

$\tt\dashrightarrow 6 \hat{j}.$

$\rule{200}1$

Taking Vector-3.

We have, Two Compounds, Let A and B.

• Angle be 53°.
• Compound be (A) 5 Sin53°.
• Compound be (B) 5 Cos53°.

Compound A.

$\tt\dashrightarrow 5 \sin53 \degree.$

$\tt\dashrightarrow 5 \times \frac{4}{5} .$

$\tt\dashrightarrow - 4 \hat{j}.$

Compound B.

$\tt\dashrightarrow 5 \cos53 \degree.$

$\tt\dashrightarrow 5 \times \frac{3}{5} .$

$\tt\dashrightarrow 3 \hat{i}.$

$\rule{200}1$

Now,

Sum of all three Vector.

$\tt \dashrightarrow V_1 + V_2 + V_3 = Required \: Answer.$

$\tt \dashrightarrow 6\hat{j} + 6\hat{j} - 4\hat{j} - 6\hat{i} + 8\hat{i} + 3\hat{i}$

$\tt\dashrightarrow8\hat{j} +5 \hat{i} .$

Therefore, the value of three Vector be 8j + 5i.