Show that the vectors 2 i -3 j +4 k and -4 i +6 j -8 k are collin… - Vidyadip

Question

Show that the vectors $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$ are collinear.

✓

Answer

Given the position vectors $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$Let $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$
Then,
$\vec{\text{b}}=-4\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$
$=-2\big(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)$
$=-2\vec{\text{a}}$
Hence, $\vec{\text{a}},\vec{\text{b}}$ are collinear.

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 "5 Marks Questions" 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

Using the method of integration find the area bounded by the curve |x| + |y| = 1
[Hint: the required region is bounded by lines x + y = 1, x - y = 1, -x + y = 1 and -x - y = 11]

Find the point on the curve $y^2= 4x$ which is nearest to the point $(2, -8).$

Differentiate the following functions with respect to x:
$\frac{\sqrt{\text{x}^2+1}+\sqrt{\text{x}^2-1}}{\sqrt{\text{x}^2+1}-\sqrt{\text{x}^2-1}}$

Differentiate the following functions with respect to x:
$\log(3\text{x}+2)-\text{x}^2\log(2\text{x}-1)$

Solve the following differential equations:$\frac{\text{dy}}{\text{dx}}=\text{y}\tan2\text{x, y}(0)=2$

Show that the following system of linear equation is inconsistent:
$2x + 5y = 7$
$6x + 15y = 13$

The equation of tangent at (2, 3) on the curve $y^{2} = \text{ax}^{3} + \text{b is y = 4x - 5}. $ Find the value of a and b.

For the following differntial equations verify that the accompanying function is a solution:

Differential equation	Function
$\text{y}=\Big(\frac{\text{dy}}{\text{dx}}\Big)^2$	$\text{y}=\frac{1}{4}(\text{x}\pm\text{a})^2$

Find the area enclosed by the curve $\text{x}=3\cos\text{t}, \text{y}=2\sin\text{t}.$

Evaluate the following integrals:
$\int\limits^{\frac{\pi}{3}}_{-\frac{\pi}{3}}\frac{1}{1+\text{e}^{\tan\text{x}}}\text{ dx}$