Vector Algebra · Mathematics · KCET

$$|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144$$ and $$|\mathbf{a}|=4$$, then $$|\mathbf{b}|$$ is equal to

If $$\mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0$$ and $$(\mathbf{a} \times \mathbf{b})+(\mathbf{b} \times \mathbf{c})+(\mathbf{c} \times \mathbf{a})=\lamb...

If $$|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$$, then

The component of $$\hat{\mathbf{i}}$$ in the direction of the vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ is

If $$|\mathbf{a}|=2$$ and $$|\mathbf{b}|=3$$ and the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$ is $$120^{\circ}$$, then the length of the vector...

If $$|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$$ and $$|\mathbf{a}|=3$$, then $$|\mathbf{a}|$$ is equal to

If $$\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$, then express $$\beta$$ in the form $$\b...

A vector a makes equal acute angles on the coordinate axis. Then the projection of vector $$\mathbf{b}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+\hat{\mat...

The diagonals of a parallelogram are the vectors $$3 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$. and $$-\hat{\mathbf{i}}-2 \hat{\mathbf{...

If $$\mathbf{a} \cdot \mathbf{b}=0$$ and $$\mathbf{a}+\mathbf{b}$$ makes an angle $$60^{\circ}$$ with $$a$$, then

If the area of the parallelogram with $$\mathbf{a}$$ and $$\mathbf{b}$$ as two adjacent sides is 15 sq units, then the area of the parallelogram havin...

The two vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$$ represent the two...

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are unit vectors and $$\theta$$ is the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$, then $$\sin \frac{\theta}...

If $$|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6$$, then $$|\mathbf{b}|$$ is equal to

If the vectors $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\lambda \hat{\...

If $$|\mathbf{a}|=16,|\mathbf{b}|=4$$, then $$\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=$$

If the angle between $$\mathbf{a}$$ & $$\mathbf{b}$$ is $$\frac{2 \pi}{3}$$ and the projection of $$\mathbf{a}$$ in the direction of $$\mathbf{b}$$ is...

A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$-2 \hat{\mathbf{i}}+\hat...

$$[\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=$$