Question:
If \(\overset{̄}{a} = 4\hat{i}+\hat{j}+\hat{k}\), \(\overset{̄}{b} = 2\hat{i}+\hat{j}+2\hat{k}\) and \(\overset{̄}{c} = 3\hat{i}+4\hat{j}+5\hat{k}\), then \((\overset{̄}{a}+\overset{̄}{b})\cdot (\overset{̄}{b}+\overset{̄}{c}) =\)
If \(\overset{̄}{a} = 4\hat{i}+\hat{j}+\hat{k}\), \(\overset{̄}{b} = 2\hat{i}+\hat{j}+2\hat{k}\) and \(\overset{̄}{c} = 3\hat{i}+4\hat{j}+5\hat{k}\), then \((\overset{̄}{a}+\overset{̄}{b})\cdot (\overset{̄}{b}+\overset{̄}{c}) =\)
Show Hint
Add the vectors first, then take the dot product.
Updated On: Oct 1, 2026
- \(30\)
- \(21\)
- \(61\)
- \(10\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Add
\(\vec a+\vec b = (4+2)\hat i+(1+1)\hat j+(1+2)\hat k = 6\hat i+2\hat j+3\hat k\).
Step 2: Add again
\(\vec b+\vec c = (2+3)\hat i+(1+4)\hat j+(2+5)\hat k = 5\hat i+5\hat j+7\hat k\).
Step 3: Dot product
\(6\cdot5 + 2\cdot5 + 3\cdot7 = 30+10+21 = 61\). Option (C).
Final Answer:
The value is 61. \[ \boxed{\text{(C)}\ 61} \]
\(\vec a+\vec b = (4+2)\hat i+(1+1)\hat j+(1+2)\hat k = 6\hat i+2\hat j+3\hat k\).
Step 2: Add again
\(\vec b+\vec c = (2+3)\hat i+(1+4)\hat j+(2+5)\hat k = 5\hat i+5\hat j+7\hat k\).
Step 3: Dot product
\(6\cdot5 + 2\cdot5 + 3\cdot7 = 30+10+21 = 61\). Option (C).
Final Answer:
The value is 61. \[ \boxed{\text{(C)}\ 61} \]
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Product of Two Vectors Questions
- If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:
- If \( \mathbf{a} \) and \( \mathbf{b} \) are two non-zero vectors such that the angle between them is \( 60^\circ \), what is the probability that the dot product \( \mathbf{a} \cdot \mathbf{b} \) is positive?
- If \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \), find the unit vector perpendicular to both \( \vec{a} \) and \( \vec{b} \).
- Find the angle between non-zero vectors \( \mathbf{a} \) and \( \mathbf{b} \) if their dot product \( \mathbf{a}\cdot\mathbf{b} = 0 \).
- Find the unit vector perpendicular to both \( \vec{a} = 2\hat{i} - \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + 2\hat{j} - 3\hat{k} \).
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions