If 3 hat{i}+3 hat{j}+sqrt{3} hat{k}, hat{i}+h | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\vec{a} = 3 \hat{i} + 3 \hat{j} + \sqrt{3} \hat{k}$, $\vec{b} = \hat{i} + \hat{k}$, and $\vec{c} = \sqrt{3} \hat{i} + \sqrt{3} \hat{j} + \lam

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let $\vec{a} = 3 \hat{i} + 3 \hat{j} + \sqrt{3} \hat{k}$, $\vec{b} = \hat{i} + \hat{k}$, and $\vec{c} = \sqrt{3} \hat{i} + \sqrt{3} \hat{j} + \lambda \hat{k}$.Since these vectors are coplanar, their scalar triple product must be zero, i.e.,$\vec{a} \cdot (\vec{b} 	imes \vec{c}) = 0$.This is equivalent to the determinant of the matrix formed by their components being zero:$\begin{vmatrix} 3 & 3 & \sqrt{3} \ 1 & 0 & 1 \ \sqrt{3} & \sqrt{3} & \lambda \end{vmatrix} = 0$Expanding the determinant along the first row:$3(0 - \sqrt{3}) - 3(\lambda - \sqrt{3}) + \sqrt{3}(\sqrt{3} - 0) = 0$$-3\sqrt{3} - 3\lambda + 3\sqrt{3} + 3 = 0$$-3\lambda + 3 = 0$$3\lambda = 3$$\lambda = 1$

If $3 \hat{i}+3 \hat{j}+\sqrt{3} \hat{k}$, $\hat{i}+\hat{k}$, and $\sqrt{3} \hat{i}+\sqrt{3} \hat{j}+\lambda \hat{k}$ are coplanar, then $\lambda$ is equal to

Similar Questions

When the engine is switched off,a vehicle of mass $M$ is moving on a rough horizontal road with momentum $p$. If the coefficient of friction between the road and the tyres of the vehicle is $\mu_k$,what is the distance travelled by the vehicle before it comes to rest?

Inheritance of skin colour in human is an example of

The inverse point of $(1,2)$ with respect to the circle $x^2+y^2-4x-6y+9=0$ is

The major product of the following reaction is

The equation of a straight line,perpendicular to $3x - 4y = 6$ and forming a triangle of area $6$ sq. units with the coordinate axes,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module